Not sure he wants the attention.
All of Hollywood works off of attention. It's their currency.
He is rich, sure, which is how he got the airplane in the first place.
Harrison Ford has a small fleet of airplanes, which you need to be rich to keep in the air. The Ryan PT-22 by itself is fairly inexpensive (I found one online for $70K), a middle class person could afford one. It's probably the cheapest plane he owns. People like H.F. buy these for the open cockpit experience and the unique sound of a 5-cyliner radial engine.
