It makes sense that we don’t elect a fed chairmen, but if the fed chairmen doesn’t report to any elected official then where do they get their authority?

Supreme Court Judges are appointed by elected officials, but then don’t report to anyone. Maybe a fed chairmen is like that? But there is no constitutional office like that. Surely congress can’t make up offices which are then untouchable?

I don’t want trump playing transactional games with the FDA either, but I don’t see how that can be balanced with the powers. He is the chief executive.

I mentioned in another comment that one angle that would make more sense than arguing that agencies are “independent” is to argue that trump is not enforcing the law already written by congress, so taking away the power of the legislature. That seems like a more fruitful take.