CPUs designed for Operating Systems

That Linux and MS Windows are two opposites most of you will already know. When downloading a Linux distro one can choose between multiple CPU compiles, one for x86 CPUs, one for 64bit CPUs, one for PowerPC CPUs and probably a few others.
This is because different CPUs have different instruction sets and the Operating System needs to be compiled the right way to use these instruction sets.

Now what if we could turn this concept around and design the CPUs so they have the instruction sets the Operating Systems want? Sounds strange doesn't it.
Well let me tell you it does exist apparently. I received an old Compaq PC from a neighboor, he didn't need anymore and he knew I could probably use some parts, so he donated it to me. I was getting all the still useful parts out of it, floppy disk drive, cd-rom drive, sd-ram, cables, etc.
The CPU was passively cooled and had a nice heatsink, which a friend of mine was looking for for some time, so I decided to pull it of the CPU. And there it was a nice AMD-K6 looking me right in the eyes.

Nothing special about that, but when I examined the CPU a bit better after disposing it of the coolpaste I noticed something very strange. This CPU was designed for a specific Operating System, apparently AMD designed these CPUs for a specific Operating System.