They already are, via cabinet members and their deputies/undersecretaries. Those people are appointed by the president, but need to be confirmed by the Senate as a check on the president's power.
Trump is doing another end run around the confirmation process with his "liaisons".
Well, some of them are, indirectly. But there are also those allegedly independent agencies (which, although maybe not a bad idea, is probably unconstitutional—we don’t have a fourth branch).
Seems fine that the bureaucrats to whom executive power is delegated should be answerable to the executive.