They're not "accountable to nobody". Assuming they have the votes, congress can revoke any law, at any time, for any reason. And typically laws specifying the appointment of specific people also have provisions for removing that person.

The reason for this is stability. Congress, businesses, international allies, and most US citizens typically don't want things to dramatically change every new presidential administration. And the primary way to ensure that stability is to make it so the same people are working in various government offices from administration to administration. And I think people are quickly learning why that stability is desirable, as the current administration attempts to dismantle it with no consideration for the consequences.