Conceptually this is very similar to the question of whether or not you should squash your commits. To the point that it's really the same question.

If you think you should squash commits, then you're only really interested in the final code change. The history of how the dev got there can go in the bin.

If you don't think you should squash commits then you're interested in being able to look back at the journey that got the dev to the final code change.

Both approaches are valid for different reasons but they're a source of long and furious debate on every team I've been on. Whether or not you should be keeping a history of your AI sessions alongside the code could be useful for debugging (less code debugging, more thought process debugging) but the 'prefer squash' developers usually prefer to look the existing code rather than the history of changes to steer it back on course, so why would they start looking at AI sessions if they don't look at commits?

All that said, your AI's memory could easily be stored and managed somewhere separately to the repo history, and in a way that makes it more easily accessible to the LLM you choose, so probably not.