That is a technique that is often used to impose frugality and get savings [1] out of the rest of the execs by setting an example. If he flies coach well then so do a hundred others.
[1] I knew a guy who owned a small company and bought a low end car until he had locked up his union contract. He knew if he was seen with a nice car it was going to cost him a boat load.
Likewise in my old school company years ago I never even drove up to the business in my nice car and I went out of my way to hide it's existence. It goes along with staying late and arriving early to set an example.
I'll take Uber pools, walk, or take public transit even though I'm technically no restriction on my transportation spending. Likewise, unless I'm taking my team out to dinner, I'll usually grab a $10 gyro or something instead of going to a nice restaurant.