There's a lot to process here, from the question (and the examples therein), the comments and the answers. I'll try to divide this answer in order to organize my thoughts.
First and foremost:
- Is deleting a question while it is still on hold too quick?
This general question does not have a clear answer, mainly because people have different priorities. Risking being too reductionist, I think there are people that prioritize cleanness of the site, and there are people who prioritize a welcoming environment to the site. Both are valid points of view which should not conflict, but usually do for obvious reasons.
Talking about my point of view, I frequently oscillate between two thoughts:
1: Most things are non-salvageable, and thus it is a waste of time to try and attempt to heal everything.
2: I do not want to exclude people from a group simply because of lack of acquaintance with said group.
To be clear, this is in reality a false dichotomy. But in terms of large-scale behaviour, it is a good approximation, in the sense that if you want to significantly erase bad content you must allow yourself not to enter too personally in them (as reference, see discussions about downvote explanations: one of the arguments is that necessary comments would create a barrier for downvoting). But an answer must be given, so I will get to the second point.
- The examples.
Personally, I think some of the examples were harshly treated. So, with respect to those examples: yes, I think the deletion was rather quick. I know that MSE's informal policies change with time, but my very first question would probably be on that list if it was made today (I think it is quite similar to this and this examples, and many others). If I could recall my train of thought in the time, my conception of mathematics was of a frigid and formal discipline. If my question was well-stated, clear and succint (and dry), it would be good. MSE helped me in part in understanding how context and communication is important to mathematics. Specifically, that single and simple $4$-word question from Did in the comments may have resulted in huge consequences. If he said something like: "We are not here to do your homework" like I've already seen people saying, I would probably refrain from asking anymore (curiously, it was not a homework). If my question was hastly put on hold and deleted, it would have probably been worse. This may happen more often than not, and this worries me a bit.
- In general.
Being honest, there is a lot of garbage in this site. It is good that we have people who are willing to basically work for free for the maintenance of this site's well-being. In general, I personally think that there should not exist a
time gap for deletion, and it is good to be this way.
But I think that it is worth mentioning that if you spend too much time on a job, your patience will eventually suffer from that. Seeing repetitive patterns will inevitably make you conflate things. It is natural instinct. For instance, you may see any question which does not provide what the person has tried as worthy of deletion. You will look at a question without LaTeX with disregard. It is good to bring this kind of discussion up so we can refresh our decision making. As is clear in the examples, there are a number of people who are quite engaged in the process of deletion/closure etc. I am grateful for their work, a work that I only occasionally do. My only concern is that if I, who do not partake in deletions so oftenly, have fallen for those "sins" of bias, I think it is not unreasonable to say that this may happen to those that do this recursively. The thing that I ask of them is only to listen with open ears the concerns of people who are not that engaged with deletion, and to consider things like those that I said in the previous "point".
I think it is also worth saying that I personally think that the deletions/closure etc as done today are good in general. This whole discussion is about improving them even further. We have a good site, with good community and with a good purpose. This leads me to my last point.
- An important observation.
This is a little off-topic with respect to the question, but pertinent due to the comments etc.
I feel there is a lot of hostility sometimes in meta. I understand that for some of us, this website is a very significant part of their life and thus we hold it to heart, leading us to feel threatened or even attacked when our point of view regarding it is challenged somehow. However, I think that it is important to notice that:
If someone comes to meta to discuss, they want the same thing as you: to improve the site. They are not your enemy, they are your ally.
Different points of view should not change that.