All attention is monetizable. Maybe you become the finance guy who may have laundered money for the narcolumbians, or maybe you become the lawyer that kept the mob boss out of jail. But that's perception, not necessarily reality. In any case, you're the guy that gets to charge more because you have more clients.

I'm kind of curious, if you're willing to give a general corner of industry. I can't think of anything that doesn't have "bad boy" characters. Seems like any federal agent kind of person would attract attention from the CIA. A doctor maybe? Still seems like someone willing to write off-topic prescriptions would command more salary.

It's actually kind of tough to think of a profession that needs to be perfectly ethical, and also appear to be perfectly ethical. Aerospace designers kill test pilots. SEC agents that appear to be on the take probably get bribed more often than the squeaky clean.

Maybe there's some corner of insurance that having a reputation would endanger your employer somehow. Everything i can think of right now implies higher salary.