When you know you definitly do not have time for an answer deleting it might unload your mental burden. Keeping hundreds of unamswered messages around might feel like an unresolved issue.

There's no functional difference between "not looking at it ever again" and "deleting it".

You should understand when they say "delete" that they mean "remove from their queue", whether it still exists in an "archive" folder, backups, trash, ... is irrelevant.

Liking to have clean and empty inbox isn't related to limited memory