I don't like to tell people to use extensions, but ublock origin (or any other extension that allows you to block elements on a page, I assume?), is incredibly handy when it comes to filtering out lots of annoying things on all kinds of sites. The recent comment box doesn't show up for me, but with it and basically anything you don't want to see, you can just right click and "Block Element" though it might take a couple tries before you get the right element.

Here are some lines you can add to your custom filters in ublock (I use FF):

! Gets rid of comment counts on archive/author/etc pages:
archiveofourown.org##.comments:nth-of-type(4)

! Gets rid of comment count showing on the actual fic page:
archiveofourown.org###main > .work > .wrapper > .group.meta.work > .stats:nth-of-type(10) > .stats > .comments:nth-of-type(5)

! Gets rid of the kudos left by/leave a comment/comments left by other people section entirely (the end of the page is just the end of the fic):
archiveofourown.org###feedback