In most cases, you have that luxury, you can make an edit whenever you need to. Only when an answer gets deleted can you not improve it; only when the question is closed can you not leave another answer.
As for when questions and answers should closed or deleted, there are several valid answers and opinions on that, but one of them is: they should be closed or deleted when a moderated deems they should be closed or deleted. Sometimes immediate action is necessary (such as when spam or porn is posted, or when an answer of exceptionally low quality needs to be dealt with).
Oh! Quality! I opened that can of worms again, didn't I? Please, no more arguments about judgemental snobs, and let's not debate whether or not your answer was of "low quality" (however, I think it got three downvotes for a reason – and no, I wasn't one of those downvoters). There are several checks and balances in place in the system. All it takes is five members with enough rep to reopen a closed question, and three members with enough rep to undelete an answer. If the moderators act too hastily, there are ways to overturn their decisions.
Do I agree with every decision they make? Hell, no. But the moderators work hard here, fighting sock puppets, removing spam, reviewing flagged posts, dealing with over-the-line comments, and – gasp! – maintaining a level of quality. All of this takes time, and they're not paid for their services. It's about time somebody recognized that, with the giant cry-fest we've had here in meta over the past week. If you think every new user needs to be coddled with a welcome wagon, then step up to the plate and do that work. It's called a community for a reason.
You asked, “Is it truly expedient to have such a fast turnover time?” 99% of the time, yes. Sure, maybe in this particular case, you can't fix your answer, because it's been deleted, and you can't post a revised one, because the question's been closed. But I see no need to revamp the entire system to account for this one perfect storm of unfortunate events.