The only constructive use for comments is to ask for clarification of a question or answer. Such clarifications should then be edited into the question or answer.
So, any given comment should quickly become obsolete.
So, I propose a sweeper bot that deletes all comments more than a month old.
And to anticipate the howls of protest: if there is any content in comments that you value, then put it into question or answer bodies right now.
I do appreciate that saying this here on this site is a losing battle, because meta.SO has an embedded culture of commenting. So even though month-old comments are clutter across just about the whole network, meta.SO cannot and will not recognise that. Sometimes the needs of meta.SO, and the Stack Exchange network, coincide. And some times they do not.
My thanks to the commenters for pointing out that people have already tried to justified the keeping of comments; reading this attempts at justifications emphatically shows that the collateral damage would be absolutely tiny compared to the advantage of removing all the clutter.