ChatGPT (at least, the paid version) does do this. But the UI doesn't emphasize it very much, and there's no way to visualize the tree of conversations.
If you hover over your message, an edit button appears. Editing your message fork the conversation, and creates a pagination thing to the left of the user icon.
For the thumbs, this does not seem to change the conversation in any way - ChatGPT does not react.
For editing (this is new to me, so TIL, ty!) - it seems to share memory across threads in a few naive tests I just did, so almost there, but not entirely.