Hatunen writes:

It's quite possible that one could have one's own private jet and
fly it with a private license.

Yes, but the fact remains that hardly anyone does this. John Travolta does it.
Arnold Palmer does it, too. Harrison Ford can do it, but I'm not sure if he
actually owns a jet. Lorenzo Lamas simply has a CPL, though (and I don't know
if he owns a jet, either).

Private pilots are a tiny elite to begin with. The ones who are also certified
to fly jets and have their own jets to fly are so rare that they're scarcely
on the radar, QED.