A major difference between FBI agents and most other government positions, is that FBI agents don’t get to decide where they want to work. They list their “preferences” about what city they would like to work in and then those preferences are largely ignored. In other words, the local cost of living whenever they end up is completely out of their control.
It doesn’t matter if the agent lives in Phoenix, and listed it as their top preference, the LA, NY and Chicago branches are the largest, so that’s where many agents will end up. What might be a great salary for living in Phoenix, is probably totally unmanageable for living in NYC.