As you have discovered there is something more going on inside the factory amplifier. That is because there is more in that silver box than just an amp. Essentially all of the filters are now out of your system so you are free of all the design elements in the factory system. That means all the time delay for all the drivers, compression circuits to protect the drivers, eq/filters, and, virtual center channel processing. Also gone is the DSP signal mixing too.

While the amp in the car will be fed the way the wiring diagram shows I approached this from the position of the head unit wire harness for implicitly and such feeding it with two channels to drive the sub and his deck to drive his speakers. So its application correct.

As for cost cutting, it is not always the case as you submit. In the automotive space speakers are generally the place where costs are cut first because their short falls can in many cases be corrected with DSP software. Head unit performance can generally be overcome too, but in many instances the "parts" are very similar if not identical to the aftermarket units in production.

The head unit is generally seen as a combined system these days with the amplification system and what drives this is the need for something more than sound. In almost all cases the systems are presented to a company based on their criteria and technology advances tied into other systems (this is where the ides of infotainment comes from).

So for example say a car company was in talks say four years ago for a system, would they be thinking about adding a jack for an Ipod or a system to control one? What they would be thinking as they brought the car to market three years later (generally the length of time it takes form concept to production), we should have had an ipod interface, alas but one was not available at the time. So they took the approach in the next year to add a aux input jack on the new models, and only now are we beginning to see Ipod, MP3, and hard drives in the car as factory options.

Take BMW for an example, they are seen in the market as a cutting edge drivers car with a focus on delivering high technology in their vehicles ahead of other, hence devices like iDrive, Navigation, and Logic 7 (surround sound in the car) are presented as leading performance advantages offer their competition. The are willing in most cases to push their partners to deliver the best experience and deliver it on time, at budget, and hit the performance target. Others companies might look at it from a cost of content for a vehicle, such might have been the case in the Crossfire, again Chryslers decision. This might have been done to keep costs in line, other companies were not able to deliver a product on their timeline, or they felt their target customer would not be interested in the additional items and simply chose to allocate those costs to other items in the car.

Sure if we all could go back in time and change the world we would want better, I would want a MyGig in my Crossfire SRT6.

The amp in the car is by no means equal to a much larger robust amplifier, they are simply BTL amplifiers developed with a specific use case in mind. In short they are designed to work within the system. Tuning of that system is not always the part of the brand on the radio/door, in some cases the car company will tinker with their own acoustics engineers to bring a system closer to what their customers think they want, or to overcome design changes that alter the total acoustic environment (new exhaust note, fan noise, wind noise, road noise from tires, ect.).