The reason why Honda, Toyota, etc have their own fluids is because they can control the formula.
Penzoil will randomly change the formula for the "green" coolant.
Mobil 1 also does the same for ATF fluids.
Let's say you are Honda and are using Havoline radiator fluid in your vehicles. Havoline announces that the fluid will be changing for better heat transfer in higher temperatures. If course, Havoline will not say what has changed. So, Honda will have to redo an entire series of tests to qualify the new radiatior fluid. We are talking chemical compatibility on every part of the engine the is touched by coolant: hoses, gaskets, plastic parts. Heat transfer testing will need to completed. Probably some sort of extreme life test of the coolant.
Same scenario, except for transmission fluid. In addition to chemical compatibility, Honda needs to retest all affected transmissions. We are talking requalifying everything through life test, durability, load test, This will easily cost tens of millions of dollars per affected transmission.
Coming from 25+ years of new product design and testing, this would be my best guess for OEM specific fluids. And yes, I had to completely retest products due to fluid formula changes. This can take months or even years, depending on how long the life test lasts.
So, circling back to the Amsoil question. If the OP is willing to gamble with a $7000 transmission, then go right ahead and use Amsoil fluids. Surely, the Amsoil engineers are way smarter than the Honda engineers. Keep in mind that Honda has been testing the 10 speed transmission with their ATF fluid since day zero. If any issues came up, Honda either changed the ATF formula or redesigned the transmission to fix the issue.
Ok, I decided to spend a few minutes on Amzoil's website. Seriously, this is how they test their fluids. The Honda OEM fluid has also delivered outstanding protection in my CRV, because the transmission is running strong at 130K miles.
- CVT Fluid
AMSOIL delivers outstanding protection in severe service.
AMSOIL CVT Fluid was installed in four Las Vegas taxis, each driven 100,000 miles. As shown in the belt photos below, AMSOIL CVT Fluid delivered outstanding protection in severe-service conditions.