So, most of this is coming from my personal opinion on the situation, but from everything I've seen across the site I think there are other people who feel the same as I do.
First, being a moderator is a job and with all jobs come responsibilities. There are a lot of active users who regularly vote on questions, articulate what they think is wrong with questions they're voting to close, and engage with other users on meta about the direction the site is heading in and every other topic that involves meta-discussions. However, all of those things are being done as part of a symbiotic relationship with the site; one of the reasons we who engage in doing that are doing this because it makes the site better and easier for us to use. When you're a moderator, you can't do that sort of thing out of the kindness of your heart, you have to do it because it's your job. Obviously at the end of the day the job of being a moderator isn't Earth shattering if you mess it up, but it's still a job that you are voluntarily signing up to do. I think it's understandable that a large amount of people would rather contribute on their own time instead of being required to contribute the entire time.
I'm an active user of this site and I'd like to think that most of my questions and answers have been well received, in terms of voting and general community response. In addition to that, I've tried to take a more active role in helping out new people coming to the site, because I agree with everyone else's sentiment that new user retention is difficult and if you just downvote someone's question as soon as they ask it, they probably won't be wanting to come back. In addition to that, I've tried to be as active in articulating why I vote to close questions and what the user can do to improve the question. Finally, in terms of my flagging of posts, 23 out of 23 times I've flagged a post have been found useful, 8 out of the 8 times I've flagged comments have been found useful, and the 1 out of 1 times I've flagged for rude/abusive (I don't know why this was singled out in the stats?) has been found useful via the stats on my user page. So, I'd like to think that I'm at least trying to actively contribute to helping manage the site in a productive and useful way. However, again I feel like I'm more comfortable doing all of these things from an active user perspective instead of taking on the responsibility of a moderator.
Besides what I just outlined above, I feel like I didn't run for two real reasons, one is a minor reason and the other I think is much more substantial. The first one is that I am too prone to argue in comments. It's not a good habit to be in and it's something that I am trying to do a lot less, but right now I do it way too much to be someone who has the mantle of responsibility that a moderator has. It would not make the site look good and I actively want to try and make the site as great as possible.
The second, and more important, reason has to do with my vision of the scope of the site. As a quick aside, I've lurked SE sites for years, I never really had a question that wasn't already asked so I never had the need to ask and I didn't feel the need to get sucked into the reputation chasing system by answering, until sometime last winter at least, so I'm a little bit new to the history of this site. My understanding is that a while ago virmaior was asked to be a moderator here given his background and current status as an academic philosopher. However, (and again I've gathered this just from old meta posts and some recently resurrected drama) he has a self admittedly narrow scope of what he defines as philosophy for this site and that caused issues with people in the past. From everything that I've seen, I feel like I largely agree with his scope of philosophy in terms of this site and I think that the direction I would tend to moderate towards would end up having the same caustic relationship with specific and potential users who disagree.
Really quickly for background, I entered undergrad wanting to double major in philosophy and computer science (leaning towards the theoretical side). After two years of doing this I realized that I was fascinated with what is currently going on in high energy physics (AdS/CFT, black hole information paradox, etc.) and I ended up getting a degree in physics and mathematics (really just a focus on theoretical computer science type math) instead. I still absolutely love philosophy and I've found that this SE has been a great place for me to continue my study/actively write about the subjects that still remain some of my favorite areas of research. That being said, I come from the background of academic philosophy (I was lucky enough to take a two graduate seminars in philosophy of language for some extra credits I needed) and I can't resist the urge to try and lean towards that with regards to this site. Because of all of this, I know that if I were to have run and been elected a moderator, I would have ended up in a similar situation that virmaior was in and, having seen how it played out, that's not at all something I want to deal with. There are a huge amount of people who come to this site that actively hate western academia and just want to start arguments. Obviously, being a moderator means you have to read everything as charitably as you can and I would not be able to do that with these specific people, having seen it as many times as I have. That isn't fair to those people, even if it eventually ends the same way.
This is more of an explanation of why I didn't run for moderator, but I do think that some of these ideas (mostly the lack of wanting more responsibility as well as the drama and hatred that comes with being a moderator) are pervasive in a lot of active users who chose not to run.
As was stated above, four people ran. Three of them mentioned explicitly that they had an agenda and wanted to force the site in a particular direction. I have empathy for most of them (one was someone who was actually just trolling) but I think that the battles they want to fight are much better done across meta first, because they are not going to win an election on a platform of "I want to change absolutely everything because there's a bias that I don't agree with." As was pointed out, one of them very clearly demonstrated that they don't have an understanding of some of the main functions of how SE sites work. That isn't a good look for anyone trying to get a moderator position, even if they aren't trying to push an agenda. I think Philip is going to do a great job, he has actively been encouraging people to improve questions and has been a voice on meta discussions as well. If it turns out he is horrible, I'm sure it will come up on meta and there will be a long community discussion about it.
So I would conjecture, and this is obviously just my conjecture, that the issue is not that we have a small user base, but that people just don't want to be moderators. Having a small user base obviously has a hand in the situation, if there are less people then there are just less people to try and do something, but even if there were only 20 people on an SE, there's always a chance that all 20 of them would want to run. I genuinely think that philosophy is a hard topic for an SE site and I think that is reflected in how many different opinions there are on the site's scope and future direction. If someone wants to take up the responsibility of steering the ship then I will try as hard as I can to communicate with them and hope the situation goes well, but steering is not something I want to personally do at this moment. I believe a lot of other people feel the same.
P.S. This is already too long of a post (one of my other flaws is my answers are too long) but I'll try to articulate one last point to try and explain what I mean by all of what I've said. A while ago there was someone who asked a question and the entire gist of the question was "all people on this site do is link to wikipedia in their answers, nobody is actually doing philosophy. This is disgusting. How can you call this philosophy?" I don't really want to even begin to articulate how I feel about that question, so I'll try to just be neutral and say: this site is not about doing philosophy, it's about answering questions about philosophy. The user who asked that question was told that fact multiple times, because he continued to be transgressive about "how decadent western philosophy is since it's become the equivalent of wikipedia" and I will be as honest with you as I possibly can: I do not want to deal with users like that. There is no bone in my body that wants to deal with that situation or has the patience to be charitable and try to be nice to them. That's a flaw in myself, but it's one I can recognize and that actively makes me not want to be a moderator.
P.P.S. Everything that is going on with this question is exactly what I'm talking about in this post. The original question absolutely violated the be nice policy, and the OP said as much in the comments when they said "I knew it would offend the guilty". After that fact was pointed out they continuously got defensive, saying "this is a forum I can post what I want, you're just trying to censor me because it offends you and you're scared of the truth," then someone else who also doesn't like the moderators comes in and just joins in with irrelevant comments about how the moderators are going to censor this post because they are "pushing an agenda" (half of the comments towards the end have absolutely nothing to do with trying to improve the question or point out the flaws, they're just agreeing that people who don't like the question are the people the question is talking about) and then, as has been the case multiple times recently, the comments devolve into a weird sort of defense of anti semitism: "The irony is that the people doing the most to promote anti-semitism may be the Jews themselves." (What on Earth does that statement have to do with the question being asked?) When someone goes in and cleans up the comments, there are just going to be more comments decrying censorship.
That post was clearly against the rules and all the OP wanted to do was argue about being prosecuted by the moderators for posting "truth that they disagree with on a philosophy forum," ignoring the fact that SE is not a forum which was pointed out multiple times. Who wants to deal with this? I guarantee, as has been the case before, the OP will post more questions like this and get in more arguments until they eventually leave the site after denouncing all of the moderators as perverters of truth.