Pervasive example:
Client-side sessions via signed tokens prevent providing a list of active sessions with details and the ability to end them. It's useful for both the user and administrators to have them in the database. It feels cleaner to not track it properly but it isn't.
Even having only a counter for each account is essentially giving up on doing it client-side.
What if the database has to be rolled back to a backup?
Do you rotate the key and invalidate client-side state entirely?
It's a problematic approach overall, I think. Not a fan.
For the Twitter site, as an example:
Settings → Security and account access → Apps and sessions → Sessions
If simply simply signed a user id + date pair with a key, they couldn't provide this. This tends to be where sites start going wrong. Next is a shopping cart, etc...