> Although I would guess a determined attacker could find it out given sufficient research.

You don't have to be determined; a college freshman on a lark found Musk, Gates, etc. and made Twitter accounts. This information is intentionally public; you can browse recent plane registrations at https://registry.faa.gov/aircraftinquiry/Search/RecentRegist..., export it to CSV, with full name and address of each owner.

I get a text message whenever my dad is seen in the air.

@elonjet isn't the problem here. (IMO, there isn't a problem.)