I, personally, am very much in favour of this possibility.
It has become a common trope that we have to heavily moderate comments and answers, sometimes simply because of people becoming involved, other times because of them going off the rails.
This is often linked to the nature of the question itself. In a sense, this is a self-reinforcing process: People like to get involved in controversial topics, this makes them interested in and looking into controversial questions, which lets them be on the Hot Network Questions bar, leading to more people getting aware of and interested in the controversial question, leading to even more problematic answers and comments. Protecting the questions has proven to be a pitifully useless tool for preventing this.
Also, we often have people not understanding why we act the way we do in this kind of question, leading to quite a lot of flags and meta questions like this and that.
Adding this note would remind people of the rules in place and possibly prevent an excess of comments (and answers), but definitely, make clear the playing rules the moderators are following when it happens. In other words, it would be a nice handy tool for not being forced to repeat the rules over and over again and remind everyone about the purpose of this site.
If anything, a link to this post for comments (because it cites the relevant part and links to the original source) and maybe to the help center directly for answers could further help and legitimise the notice itself and actions taken according to it by pointing out the rules and where they are to be found.
I would argue for using the links as follows, to highlight the ONLY parts and establish the desired effect, pointing out that we do not have to bother arguing why every time we take action in that question thread:
Controversial Post — You may use comments ONLY to suggest improvements. You may use answers ONLY to provide a solution to the specific question asked above. Moderators will remove debates, arguments or opinions without notice.
One last comment, as this might be misunderstood considering recent discussions: Those rules are in fact effective for all questions, comments, and answers. All the time. It's just that we can give more leeway in non-controversial questions. Nobody likes overly pedantic mods (or so it seems).