I'm not saying that we should delete every comment ever... but comments serve a purpose... they are designed to ask for more information or clarification... comments like the one you mention are pointless. No, one of them doesn't hurt anything but that comment is literally one of the purposes of upvoting (as you say).
If we allow it, we're liable to have such a comment on every single question on the site... and possibly multiple of them. One doesn't hurt anything - but people seeing that they're "acceptable" sets a precedence and the next thing you know, we've got hundreds of them and cleaning them up after the fact becomes tedious.
From Meta.SE, this question and the questions it is a dupe of discuss methods of allowing users to say "me too", generally to prevent such comments or answers which are not appropriate... and the universal response is - this already exists, it's called upvoting.
Dan Bron: That button already exists, it's an upwards-pointing triangle juuuust above the question's score.
Robert Cartaino♦ RothMedia, up-voting serves a lot of purposes, and using it to add more weight/importance to the question is one of them. It may not be as explicit as a separate 'me too' button, but scattering a selection of buttons across a question for each of the reasons why you think it deserves more attention would only dilute the signal that determines the sort. Giving users more buttons to push and axes to vote on would likely have the opposite effect of what you are looking for. See a good question? Up-vote. Simple and effective.
I don't see any reason we should accept users cluttering up the questions with comments that are unnecessary.
Similarly, comments that are obsolete should be removed... If a comment requests clarification and the OP adds it, no one should expect that comment to remain. It'd be awesome if people deleted them on their own but if it's flagged, there's no reason not to remove it.
None of this means that we should expect our mods to burninate every comment that is obsolete, too chatty, or not constructive instantly... there's no way that they could keep up with that but if you see a comment you feel should be removed for one of these reasons, flag it.
The privileges page explains how comments should be used, if you want to see the "official" rules...
This question seems to be asking whether we want our mods to ignore all comment flags reasons (other than spam/offensive) - These comments are supposed to be deleted by SE policy and that's why these comment flag categories exist. Declining flags constantly because we, as a community, have decided to ignore policy regarding usage of the comments section sends really mixed messages to our users.
Comments can be clutter. They detract from the actual content of the site. There is no value to saving comments like:
- Me too!
- +1, great answer.
- Thank you!
- -1, this is bad. (with nothing else)
We should follow SE policy and delete them when seen/flagged.
The other two sections are fine but we can not condone pointless comments here.
- Long discussions: Move to chat
- Off-topic (to the current question) discussions: Migrate to chat (remove the comments and take them into chat)