Lol I met the guy who co-launched the new weed product line with Mike Tyson by sitting next to him on a WN flight and he's a millionaire living in the LA hills and this was a route that JSX does. I also know rich people who fly Spirit/Allegiant/Frontier when that is the best non-stop for them to take, as they care more about their time than anything else. I'm sure LCCs or anything without first class is not their first choice, but getting there ASAP is always their first choice.
Granted, most people I know personally who are rich did not make their money in traditional ways so I guess they are probably way more chill than someone who did it running a fortune 500 company. But the point is, they don't care as how they get there as much as when they get there. Within reason, I'd assume.