bitflipper
You'd think that in-ear monitoring would have solved the appease-the-musicians conundrum. Once they stick in their IEMs they have no way of knowing what's coming out the front. Turn the guitarist up in his mix, the bass player in his mix, and make the singer think he's alone on the stage. Everybody's happy.
 
I have never actually tried such a thing in a live venue. But it works in the studio.

Our P&W band just went to in ears at the start of the year.  We have some quality equipment with each performer able to control their own monitor mix.  We also avoid amps on stage.  The bass is DI and the electric is usually DI though a Boss type effects board, although we have a small 15 Watt Vox that is mic'ed.
 
The only real drawback is that the band literally has no idea how they really sound.  Also, the drums aren't quite isolated enough, so everything has to come up to blend with the direct sound from the drum kit - that will be fixed with a new and better drum booth.
 
We have 4 FOH guys that rotate and each one mixes a bit differently (you can tell which one the guitar player is.)
 
I was visiting another church over Christmas and they have a fantastic set of performers, but they suffered from an untrained FOH (and crappy mains.)  The mix was really harsh and not well balanced.