I’m puzzled, as it does appear to be doing that here on Meta.
I tried on my site, but it literally just repositions the columns in the table view.
If I re-order by clicking a different column in the table view, then switch to card view, it retains that order until I leave the page and return. A fresh visit to either the card or table view orders it by likes_received again, no matter what order the the columns are in.
Unless maybe there’s some scheduled job that needs to run, to store the change…?
(I know a partial workaround would be editing the Users sidebar link to /u?cards=yes&order=days_visited but it’d be nice to have config options for default timeframe too.)
EDIT: either I missed your closing line, or you added it while I was composing. Yes, /u?cards=yes&order=days_visited&period=yearly does the trick. (And looks like /u?cards=no&order=post_count is what’s happening on Meta.) I’m happy with that for the moment! But still, admins might like some added config options.