If the President is elected, and the President holds the power to staff the executive branch (subject to the approval of Congress and the restraints on arbitrary exercise of the CSA of 1883 and CSRA of 1978), then in what sense is the bureaucracy uncontrolled by the electorate?

Or do I misunderstand the American system of government?

The CSA and CSRA were both implemented to put a stop to the spoils system for executive offices that existed previously.

Do you think that was better?

And if not, how would you propose re-politicizing civil service positions without falling victim to spoils again?