Very few rich people become commercial pilots. They might get a private pilot license as a hobby but generally pilots are just employees they hire to take them around.

Plenty of working airline pilots come from regular middle-class backgrounds and never served in the military. They take out student loans to pay for training, then work low-paying jobs as flight instructors or something to build up enough flight hours to get hired at a regional airline.

Those who go the ROTC route can totally get a fighter jet assignment if they want it. Once they get selected for a pilot slot, assignment to a particular airframe is primarily based on how they perform in the training pipeline.