Conversely, you could say that congress has delegated "judicial and legislative" powers to the executive, whose will is embodied in a democratically elected president.

"Gail Slater" is not a democratically elected person of any kind, and exists as a function of the executive, and hence of the president's policies. Insofar as the DOJ's anti-trust's leaders depart from the will of the elected president, it is that leader to be fired and replaced. Or else: what ever was the point of electing a president?

There's nothing in principle wrong in a president disagreeing with the execution of his executive powers, delegated to Gail, and hence firing him. Indeed, if that were not the case, the election of a president could never change the operation of the executive, making the election pointless.

If you disagree with the anti-trust decision, the issue isn't with the political mechanism by which it was over-ruled, but with the election of that president.