That was all before Commodore bought them.
If you want to know more about the origin of the Amiga, buy the book "On The Edge" where the original engineers talk about how Commodore changed after the C64 years and decided to buy the whole Amiga dev team, rather than just license the chipset. Lots of changes had to happen to turn it into a real computer.
No, the Amiga was definitely separating the functions as well. The OS was designed to handle all the hardware calls through proper APIs. The Amiga community just regularly broke Commodore's rules and used the hardware directly because the CPU couldn't enforce good programming practice, so programmers didn't give a damn and just bypassed the OS entirely. PC programmers did the same, of course, because there effectively was no OS, but hard-coding PC hardware was risky due to massive market fragmentation. The Mac suffered the most from bad programming, but according to Apple fans, their computers never, ever crashed or had any problems... right? MacOS was a step avove MS-DOS, but not by much.
The PC was a horrible machine chucked together in the cheapest way possible since IBM had little confidence in the home PC market, but had to have something out there to look competitive. The fact that it was barebones made it possible to clone, but that awful unshared bus and non-relocatable 16-bit BIOS caused nothing but headaches. Adding hardware to the bus was anything but simple. Ever recall having to manually set interrupts and DMA settings from a custom boot disk? The hardware didn't do anything for you. It was just hacks upon hacks, and nothing was standardized. It was way too easy to plug a card into the hardware bus and end up with an unbootable system since the BIOS had no understanding of mapping memory addresses and access modes to the new hardware.
The Amiga was designed from the get-go to do all that stuff properly, and the OS was fully aware of any expansion cards (if you scanned for them). The ROM could also be mapped to any memory address, and there was no need for "memory managers" like on the PC. Remember QEMM386 for the PC? That didn't just make it easy to use protected memory, it also fixed a lot of the stupid memory-mapping shortcomings of the IBM architecture. The Amiga didn't need stuff like that. If you wanted to use a different disc controller than the one built into the chipset, you were supposed to extend "trackdisk.device" with a new driver and dostype. Hitting the hardware directly was the stupid way to do that, but all the game developers wanted their clever copy-protection, so they did things the stupid way, anyway.
The only reason why the chipset became a liability is because Commodore was lazy and never really updated it. If it had changed more often, programmers wouldn't have been able to get away with their stupid hacks and would just have used the OS routines -- like they were supposed to.