I think this feature request is a good idea, mainly because I think this is a good way to try and reduce the number of identification requests that we get on this site. Sometimes I come across an identification request that I know the answer to, and I have to hold back from telling the asker because that would just encourage more off-topic questions, which just makes me feel bad! (cough Until Death Do Us Part cough).
If possible, I'd rather we be preemptive rather than reactive. In the spirit of the "Just In Time" Theory of User Behavior, I think people are much more likely to read something (e.g. "No identification requests") if it's right in their face as they're writing their question. Right now, all of the information about what's on-topic and what's not for this site is hidden away in places like Tour, Help, and How to Ask, which all sound really optional to the average user.
I think r/WritingPrompts has their sidebar text pretty figured out: A very clear "read this before submitting", and a brief overview of the most salient rules/guidelines, with additional links for more specific details. And the sidebar text stands well on its own even if the user doesn't open the links. Maybe we could change our sidebar text to something along those lines? (If nothing else, it'll make me less guilty about voting to close off-topic questions because then I'd know that the asker can't be bothered to get to know the rules, rather than just being innocently unaware that such rules exist :/)
The Hardware Recommendations Stack Exchange has gotten their sidebar text changed in the past, so it ought to be doable, although we'd need to involve the community team.
And we'd probably need to have a consensus on the exact desired wording to have any shot at this being processed.