The challenge in migrating email isn't that you have to move the existing email messages; any standard email client will download them all for you. The challenge is that there are thousands of external people and systems pointing to your email address.

Your LLMs memory is roughly analogous to the existing email messages. It's not stored in the contacts of hundreds of friends and acquaintances, or used to log in to each of a thousand different services. It's all contained in a single system, just like your email messages are.