The factory amp going to the doors are a single channel. Inside the door the factory harness splits into two (one for the tweeter and one for the woofer).

The aftermarket crossover only needs one input and provides separate outputs each with their own crossover section thus you can't use them with the same approach as the factory system.

In a nutshell the factory amplifier contains digital filters that can be manipulated to act like a crossover. What happens is the drivers in the door are measured for their response, the right filters are identifies to limit the upper and lower ranges of the woofer, the tweeter has a capacitor attached to it to roll off the midrange and bass from it. All in all it can deliver better sound this way because the designer can address the effect of the car's interior after the design.