This and another recent question seem intimately related, so I'll try to avoid repeating myself too literally and address your points WRT comments vs. edits:
1. this wastes time
I guess that is subjective, but I would have said making a comment is often easier than an edit. Put another way, if you are just correcting a typo, then sure, an edit is easier. If it is something more complex, then an edit should seem harder than a comment -- if not, I worry you are using too big a hammer (pounds nails in faster but tends to damage the surface too).
Of course, doing something one way because it is easier or faster does not always make it the best choice anyway.
2. this creates unnecessary comments (which I think should generally be avoided)
No doubt almost everyone thinks unnecessary comments should be avoided. However, I don't think it is a good idea to encourage people to make edits instead of comments on the premise that all comments are ultimately unnecessary because the ideal Q&A has no comments; first because if the powers that be thought that was so, SE would not have comments, period, and second because that is begging for disasters of a much more serious sort.
I'd rather see a few "unnecessary" comments than watch a question mutate as 3 or 4 people decide it needs to be edited.
3. the correction should usually be better if done by the one who noticed the problem than if done by the one who made the mistake
You raise a good point in so far as the questioner may decide to edit something based on a comment and misinterpret it. IMO, though, in many or most cases it is better to give them the chance and correct their attempt if necessary rather than do it pre-emptively.
4. the teaching effect should be reached by looking at the edit
There is value in that for some simple things but I would not rely on it or stretch it too far! It is probably much easier to misinterpret an edit than a comment.
"It's not a discussion forum"
This is certainly worth noting to newcomers, but I sometimes see it repeated with a bit too much zeal. To me, the point is simply to make clear the difference between SE and traditional forums. It is not to say there should be no dialogue of any kind.
As is, extended discussion is (effectively) discouraged largely by the mechanics of comments: they have to be short, you can't use a lot of features, you can't edit them past 5 minutes, and if you go back and forth you are reminded of/invited to the opportunity to chat. Currently, I don't see any serious problems with that system, or the behaviour it produces. A question or answer with 20 comments on it should not by definition be seen as something which needs "cleaning up" or "correcting". It may, but IMO it may just as easily not. Notice despite all the other restrictions, there is AFAIK no limit to the number of comments that can be made.
There are certain kinds of information best left in a comment, just as there are certain kinds of information best left in a footnote. Cramming footnotes into the main body of a text does not automatically make it clearer (or less cluttered) and can easily do the opposite.
All that said, the final point I'd make is that different people think differently and making more rules to discourage such differences is not good for any community.