I think getting to be the authority on your information would be awesome. If people hooked into your API instead of vice versa, you rarely have to update your information in more than one place. Address changes, place of work, DOB (?) - maybe these could all be achieved through an API for yourself.

There's a possibility for analytics that pulls data from all sources instead of just once (health analytics, IoT data).

There's a possibility for communication -- instead of email, maybe people could communicate through these endpoints.

All of these are just stubs of ideas, but you have a very good point. The largest use case is probably in visually representing your online data.