To answer the headline question:
Yes, there are quality requirements for comments alongside the requirement of a specific purpose.
From How do comments work?:
When should comments be deleted?
Comments are temporary "Post-It" notes left on a question or answer. You should not expect them to be around forever. Once a clarification has been made, an edit added to the post to include new information, or the issue in the comment is otherwise resolved, it is subject to deletion. In reality, many obsolete or chatty comments remain untouched due to the high volume of comments posted, but this does not mean that they can't or shouldn't be deleted in the future.
Quite often, clarifications are never made, edits never happen and the issue the comment raised is never resolved so those comments are not "obsolete". Sometimes these things do happen (or are considered by the author and rejected) and no one ever knows, so the comments are obsolete but you can't tell by looking.
So, given the explicitly stated SE reason for deletion is problematic, other criteria have to be applied. So, from When should comments be deleted? (my emphasis):
The design of each site places primary focus on questions and answers. We want all useful information required to answer a question to ideally be in an answer. How that answer was developed is largely unimportant so long as the final product of that development is valuable. How valuable it is can be determined through up and down votes on the answer.
Stack Exchange set out to "make the internet better" by creating an environment where the best information rises to the top. Asking the user to dig through a lengthy comment thread on the off chance that the information they're looking for is there goes completely counter to that mission. If we're going to allow that, we might as well just abandon this whole Q&A idea and go back to forums where readers can already sift through pages of unrelated or possibly contradictory information.
To my mind, the quality criteria for keeping comments where it is not obvious that they are obsolete or superfluous (or, obviously, offensive, insulting, or otherwise not in keeping with the spirit of the "Be nice" guideline) is:
Do they make the post (Q or A) better?
This is only partly a factor of how good the comment itself is but also affected by the comments around it. What might be a great comment if it is one of two on a question might not be worth keeping if it is the twelfth in a back and forth discussion of twenty-eight. In general, three or four comments can make a post "better" but 10 or more rarely do – it relies on the reader taking the time to wade through the dross for the nuggets of gold. Who has time for that?
What to do instead of commenting?
If your fingers are itching to reply to a comment that was a reply to your comment: stop and create a chat room. That's what they are for. Once you have the URL, you can make a comment saying "Let's continue this in chat".
Or, if you lack the 100 rep to create chat rooms or you realize you should have done it 8 comments ago, flag a comment and ask a moderator to move the comments to chat. We can do it wholesale.
Chat rooms with at least 15 comments from at least 2 participants are permanent.
However, users must have 20 rep to talk in chat – consider if your interlocutor(s) qualify.
Many people, myself included, comment when we should edit. Repeat after me: "From this day forward, I will endeavour to remember that editing other people's posts makes things better for the community and the OP. Better posts get more upvotes. More upvotes makes the OP happier."
Seriously, if you think a post would be better with something added, deleted or changed: do it!