Should topic threads stay open or be closed after 90 days?

No, closing doesn’t prevent a poster from deleting or editing there previous posts.

DenisRoy’s activity could be muted via a user’s notification settings.
(EDIT - Steve had shown that this was not working well at the time.)

ADD: Another thing I hate is when the system avatar “edits” a thread by closing it. The closed thread worthlessly pops to the top of the Latest list.