Some of us have friends online and we'd like to be able to do things like continue conversations while still being identifiably the same individual.

Also there's consideration of privilege schemes where the access is based on karma, activity, or account age. That's aside from the potential issues that could arise if someone with high privilege (supermod for example) has their identity vanish leaving a community minus whatever function they might have been performing (this user is allowed to send the bot commands, etc).

On a personal note, not having to jump through a bunch of hoops intended to screen out bad actors just to access a community or group where you were already a member in good standing.

Beyond that, there's some people who really want to express their particular identity or brand online - for example I sometimes write using a particular name. If I could no longer use that name and not even access my account to tell people that, it would not help my audience find me or my back catalogue.

Beyond all those things, having access to my post history means I can look back at things - have you never sat and looked at old diaries or photos from when your were a child? Or been reminded of some event you enjoyed? Or even just wanted to check something went down like you remembered it?