It could be useful even if they are old posts in my personal opinion. It could happen that I forget to read/manage some post, and I remember to do it only later....
However, if you want to turn off the delete button for older posts, I think it should be based on a *known* time period. E.g. posts that are older than 1 year; or older than X years, where X is an option that the admin can customize by his needs