Another consideration is that FBO's don't usually provide GPU's for free. If it's about saving money, it's a very modest savings at best.
I typically will start the APU 45 minutes before departure time on the Citation X. We need the APU for engine start anyway. Also, we are supposed to be ready for departure at least 30 minutes prior to actual scheduled departure time per our FOM. The IRS's in most of our X's need at least 6 minutes to align, and ATIS's, clearances, and programming can take over 10 minutes sometimes. And after everything's programmed, it still has to be cross-checked by the other crewmember per our FOM. Then throw in the fact that pax oftentimes will show early, it becomes clear that sometimes starting the APU 45 minutes before departure isn't enough time.
On a different line of thinking, if you have the APU, it SHOULD be used (but not for napping, watching movies, eating dinner, etc....). Mr. Moneybags didn't buy an aircraft with an APU just for bragging rights. He expects to show up to a climate-controlled aircraft on the ground. Keep cutting service to our clients and we WILL be nothing more than another airline before you know it.
And as others have mentioned, clients showing up late really mess with APU run times. It's just part of the game.
As for shutdown after departure, I don't like to do it until we're through 10K feet. The APU is an excellent backup resource, but only if it's running. Most of the time, by the time you reach cruise, if everything is running fine, it'll continue to do so. It's during the takeoff and approach phases that failures can be critical. For example, if during approach or takeoff you have a dual gen failure, you may have much less time to deal with it than at cruise. Or at the very least, things will be busier. With the APU already running during these phases, a dual gen failure almost becomes a non-event.
At any rate, it'll be interesting to see what APU policies NJA comes up with. I hope it doesn't impact customer service.