Part of the fun in a coup, for me, is when you have a few buildings in the hands of players who are either not committed (yet) to either case, or at least willing to switch sides.
This makes for fun situations ("He took that building! But is he for or against us?") and heated negotiations at the end of the coup.
With a dry "use my dice", yes, you'll save a lot of time. But at the expense of a lot of the fun.
I agree 100%, but most of the crew will not be interested in the 'wargaming' part of the coup and would probably be turned off. I think the lying and deceit of the budget and assassination process will still provide a great deal of fun.
Alternatively I also considered having players just place their dice on the different red areas, battle for control of them and then declare whether supporting El Presidente or the Rebellion.