Finance is fairly broad. People in middle management whose job is basically to deal with paper work many times say they are "Working in Finance".

Just like people working at helpdesk say they are working in "IT".

Higher finance is filled with crazy maths, if you are interested in statistics and probability then finance is the best way to make a lot of money.

Its also not "gambling,etc" - its educated decision making. People in higher management need to make a lot of very important decisions all the time. 90% of the time they just use their "gut feeling". This is where people with strong technical knowledge in finance comes in.

Where to allocate money is a very hard question to answer, you can throw a random dart at your options or bring in complex ML models. The sky is the limit.

I have no data either but one point is that the "ceiling" is higher. Meaning, a non-management programmer has a rough salary ceiling. Few programmers are paid $400k and it's not a very realistic goal.

My mathematics -> finance friends (that are very good) virtually have little to no ceiling and have already doubled my salary.

Like @wrong_variable said though, it depends what jobs and if they make it through (it's pretty competitive), so you're getting survivor bias from me.