"Sharing my data" isn't something that cross the average person's mind unless there is a checkbox they annoyingly have to check in order to check in to some European hotel which is asking you for permission to process their data, for better or worse.

In their mind, most of the times, if there is no one standing behind them when they chat with a LLM, then the conversation for most intents and purposes is private.

Obviously, us who are born with a keyboard in front of our hands, know this to not be true, and know we're being tracked constantly with our data being sold to the highest bidder. But the typical person have more or less zero concerns about this, which is why it's not a priority issue to be solved.

The average person using an LLM probably doesn't even know who Sam Altman is, nor care.

You can self-host.