You're greatly overestimating the discretion that the executive has regarding budgetary issues.
Remember that specific dollar amounts in cuts were applied to specific agency budgets. For example, if "state mediation grants" were cut by 8.2% from the Farm Service Agency under the Department of Agriculture. They can't just say "nah let's cut a few more food inspectors and keep the mediation funding." The FAA can't just unilaterally drop some of its NextGen R&D budget to shore up the Operations budget. (which includes air traffic control operations)
This is because the sequestration bill is freaking stupid, and was intentionally designed to be a stupid way to cut spending. Congress was trying to force itself to come to some kind of agreement under the threat of sequestration being stupid. And they ****ing did it anyway.