Isn’t that the whole definition of “executive branch”? They are given (by we the people) the power to choose how to execute the laws. And we elect them.

The alternatives I can think of are for laws to be executed at the whim of an algorithm, a king, a more local executive like the governors of each state, or a more distant foreign executive like the UN

No, the executive branch has a responsibility to execute the law. It's not a privilege. We elected them to perform a duty on our behalf. Do you understand the difference?

Isn't discretion a foundational principle in the exercise of the executive's functions? Or is discretion reserved only for the judiciary?