iPhone 13 Pro here — Even after multiple restarts, I cannot Select All and delete messages from iMessage. Even when deleting them individually, they still get all glitchy and come back.
Side note: I do have an Apple Watch Series 7 and iPad Pro 11 M1, not sure if imessages is glitching b/c of those somehow, but worth mentioning.
This has been happening to me since iCloud Messages was introduced. I saw a "more than (10) reports and "potential fix in iOS 16" comment in the Feedback app after I filed it as a bug YET AGAIN during the iOS 16 betas but nothing changed.
edit: sorry, in my case it is attachments (photos sent / received via iMessage) and not texts itself.