never worked on the system 10, seeing as how I have a 165, but from my limited knowledge I'll try and explain whats up.
The reason that you will be losing 2 speakers is because the aftermarket head unit only has outputs for 4 speakers unlike your factory unit which has more outputs(again, I never worked on one, so I dont know how many).
The reason that they need to do a rewire to bypass the factory amp is this:
A stock head unit puts out a low wattage signal. it needs the amplifier to boost that signal to a normal listening level. An aftermarket head unit already has an amplifier built into it. therefore there is no reason to use the factory amp, because your factory speaks wont be able to handle the wattage.
I guess the ghetto thing to do to keep all your speakers would be to splice those unused speaker lines into used speaker lines after the install. I wouldn't really recommend that seeing as how it would cut the power to those speakers.
Hope I helped a little bit.
BTW, yes, a amplifier bypass will be expensive, because the shop won't(or should not) use the factory wires. the correct way to do it is to run new wires to each speaker directly from the head unit.