… can the executive branch institute policies that will clearly result in less revenue coming in?
One way would be to administer the collection process poorly on purpose.
Another way would be to forgive or defer payments that are statutory.
Sometimes Congress expressly provides discretion to the Executive in the enabling statute. Also, some functions, such as the discretion whether or not to initiate a criminal prosecution, are considered inherently executive and part of the the Executive’s independent Constitutional authority.
FYI, “Congress controls the purse strings” usually refers to the need for Congressional approval for money to be spent, as opposed to collected.
But yea, what Tom said, the Prez has as much leeway in directing collections as the Congress that passed the original legislation gives him.