The check on prosecutorial power lies both with the Judicial branch and, in cases of a jury trial, the People. Prosecutors are not judge, jury, and executioner.

The Legislative branch gets a say by writing, passing, repealing, or amending laws.

So the three branches check each other, no need to "just trust me, bro" with prosecutors.

If the President cannot faithfully execute the laws without BREAKING them then that either means the Judicial branch should strike down the laws that are preventing that or the Legislative branch should pass laws that contain a carve out for the President. The President is not above the law, so the half-measure of the Supreme Court deciding that they are in official acts is both ahistoric and enabling despotism.