You're under the mistaken impression that you will own this data. What you are describing is akin to saying you will just export your friends list, posts, messages, pictures, etc from facebook to some other social network.
Maybe you are technically able to run your own AIs (and I guess they would somehow be supported by these other platforms?). But most people are not.
It's hard to export my friends list because there's no API for automated tools to use. AI can export your friends list today because it can see your friends list in the browser. I think the same thing will happen for chatbot memory. I don't need to run my own AI to do this. Every AI company will build their own importer.
You're under the mistaken impression that you will own this data. What you are describing is akin to saying you will just export your friends list, posts, messages, pictures, etc from facebook to some other social network.
Maybe you are technically able to run your own AIs (and I guess they would somehow be supported by these other platforms?). But most people are not.