> Why do CPU vendors implement a mode that cannot be controlled by the user?

Devil's Advocate: can you control every transistor in a good old Z80?

Of course, that's not where the goalposts are. Any piece of hardware will necessarily have limits as to the amount of introspection and manipulation that it allows in the programming model.

What Intel have done is built a "grotto" in the chip that is extraneous and deliberately inaccessible.