only the front components run off the factory amp (someone correct me).
I don't think the two door Tahoes even had a factory amp, but I could be wrong. I know in the Suburbans it's only the middle set of speakers (in the rear doors) that run off the factory amp. Front components and rear roof speakers are run directly off the head unit.
Honestly, 4x10 is a waste of space for audio , in my opinion. It is a wasted of wattage running away from your head unit. There are maybe 2 or 3 brands that carry a 4x10, and none of it is any good. I pulled mind, went with a set of 6.5 focal components in the doors, and mounted my rear pair to the b pillar behind the seats. Perfection.
4x10s are no worse than a 6x9 inherently. They're not the best speaker size out there, but calling them a waste of space and wattage is a little ridiculous. They're definitely less available due to being implemented in vehicles so rarely, but there are some good options out there. Those Kickers I linked above for example.