Fame
You could get outed as an air marshal by Kim Kardashian, but that's not the kind of PR you really want.
In fact, the whole idea is to be incognito. You don't have to lie about what you do for a living, but you're not supposed to broadcast it to the world. It's for security reasons, of course, but it also means that fame isn't likely in this line of work. If all goes well, there won't be a single incident on a flight you're on, so your cover will never be blown, and no one will even know you've been on the job in the air.
Of course, if something terrible does happen on a flight you're monitoring, and you manage to save the day, you should probably expect the press to come calling. People love a heroic tale, after all, and saving the lives of hundreds of people is about as heroic as it gets.