I do not believe that the guidelines on tree questions are clear enough. I'm inspired by a recent tree question, where the post proposes a tree and asks for specific correction (what "to" is). The question does not literally request people to make a tree, but it could be seen as a variant of such a request (such questions are sometimes closed, e.g. "Lucy reported that scientists wonder if the medicine will work"). The above-mentioned reasons are half about title problems, and I don't understand what the real issue is there. The statement There's no intuitive way to title them so they all end up as variations of "Syntax tree problem" is ambiguous. Does that mean "title them in such a way that they...", or "title them, and therefore they...". There's an underlying presupposition about titles that I'm not getting.
The main feature of tree-drawing questions which I find most useless is something that extends to various other questions not even about syntax, namely the class of "please do my homework" questions. That class of questions seem to really meet the objection of there being little chance that the question will ever help anyone but the OP, and it seems to me that "do my homework" questions themselves should be banned.
It seems to me that the third objection is a particularly relevant one, but it should be more general and also more explicit. In the case of "Lucy reported", there is no discernable general question, whereas in the question about the infinitive complementizer, there is, and the questions could even have been phrased as "what label immediately dominates infinitival 'to'?". Thus, on-topic questions should transparently generalize to some class of linguistic phenomena.
Obviously, closing vs. not closing questions about syntax trees depends on how some number of readers feel about a question, and the "Ginny thinks Harry is dreamy" question does in my opinion satisfy the desideratum of generality (it asks about the status of be-Adj phrases and whether be is a "verb").
My reason for posting this answer is to try to create a bit more guidance for posters, so that people will better understand what kinds of questions to not post, and why. The help center partially defines "on-topic" via 4 "and not" conditions, one of them being "Please make me a syntax tree" which points to this question. This therefore would be an appropriate place (if not the most appropriate place) to put clarificatory comments.