As someone who's spent some of their career in each one of these groups, I have to agree 100% with your analysis.

An interesting intersection is the Finance/Management/Business faculty. A new Assistant Professor in Finance can make significantly more in salary than a full Professor in Mathematics.

Here is some interesting data to back up my point and this is average salary. The amounts can be much higher at top institutions.

https://www.higheredjobs.com/Salary/salaryDisplay.cfm?Survey...