Hanah Volokh discusses the way that statutory qualifications can violate the separation of powers:
Both of the two appointments procedures are set up on a straightforward separation of powers principle: I’ll cut the cake, and you choose which piece you want. That is, Congress creates the office, but someone else gets to choose who fills it.
This leaves us with an important line-drawing question. Just what counts as “creating the office,” and what counts as “hiring someone to fill it”? The gray area here is job qualifications.
Clearly if congress said “the office will be filled by Harry Reid” when creating a new executive office, that would violate the separation of power, but surely Congress should have some authority to create limits to help prevent cronyism, corruption etc., so there is a need for a balance.
What Ms. Volokh has not mentioned yet is that the constitution has a good structural mechanism for creating a good balance in the Supreme Court. The legislative branch and the executive branch jointly appoint Supreme Court judges, and as a result, those judges represent the interests of both the legislative branch and the executive branch (though biased towards interests of the executive branch). Perhaps it would be better then if the Supreme Court did not consider constitutional questions when reviewing this issue, but instead made a judgment call based on ‘reasonableness’. The Supreme Court does not have any incentives to favor either branch or too much interest bias toward either branch, so it is in a good position to decide which statutory qualifications for executive branch offices are appropriate and which are not.