The issue you raise is important and comes up frequently. Let me first comment on the specific proposal.
My solution would be to allow a user to downvote/closevote if they commented on the question at least ten (perhaps more) minutes earlier.
On the one hand there are good reasons to allow users to express their view semi-anonymously as T. Bongers explains. But, on the other hand, even if we'd agree for the sake of argument that this is irrelevant or that the interests of askers take precedence, the thing is:
If you force people that do not want to comment, to still comment, they will just comment in all kinds of ways, laconic, sarcastic, humorous, tricky, you name it, but they just won't be helpful or constructive.
Because those that want to leave a constructive comment, will already do so, and those that don't, they just won't, and especially not if the system tries to coerce them.
Alright, maybe I went a bit over the top here, but still forcing to comment will not be all that effective in encouraging desirable behavior, that's a near certainty.
Now, that said why is moderation on questions sometimes swift.
For every poster that reacted well, there is one that does not react at all (and still gets an answer), or worse lashes out. At some point some decide they have been ignored and insulted enough, and they stop commenting.
Every new asker on the site just saw this: https://math.stackexchange.com/questions/ask/advice and ticked a box that they'll keep this in mind. Thus, it is not the case that we did not inform them at all. They, ignored our advice. Yes, no one reads all the text on all the websites where we tick one box or other to do what we want to do. Thus, we should not be too harsh. But, there is also no need to be overly critical of ourselves.
The downvotes are useful in that they signal to the asker and to others that there is a problem. The asker that received a down-vote might be taken aback. But maybe it could still make them realize that the page on which they just ticked a box was not just a fanciful way to say "Welcome, user!" but is actually to be taken seriously. Or also, if somebody experienced sees a post at -1, they can go there and explain if they feel so inclined.
Sometimes answers come in very quickly, too. There is concern that if one does not moderate very quickly against a question it'll be too late. See the other point above.
Volume is high, and people only have that much time and energy.
Thus, I do understand why user do not always comment. But also, I agree it is often better to comment, and I encourage everybody to leave helpful and constructive comments.
Finally, regarding the downvoting, as explained above I think a -1 can have some actual relevant and ultimately constructive effect. To pile on with more downvotes maybe does not add much in addition and might just alienate and frustrate. It also puts the user in a situation that the improving may seem hopeless.
Thus, I would say downvoting to -1 even without comment is fine and can be useful. To pile on for no specific reason does not add much, and maybe everybody pondering to cast a vote below -1 could pause and consider if it is really necessary and if there is not a better use for that vote.
Conversely, those that want to help the questioner should actually try to help and not just undo the downvote with a counter-vote, especially not prematurely, that is, before the problems were addressed. Because if that happens too much, others will feel confirmed in piling on preemptively.
