The page faulting was also on older systems, because putting those things in hardware is a lot faster than doing those things in software, plus controlling memory access really should be a privileged activity. Interrupt handling is in a similar situation, and even there, you still need some process handling the interrupt vector table. It's possible to make most of an interrupt handler a user-level process through page table and interrupt return address hacking, but for the moment, it's unfortunately rare.

As for your desire for a replacement for one exclusive, reserved kernel mode, there have been a few OSes that have tried to break that pattern. OS/2 used Ring 2 of the x86 for drivers, but unfortunately that bit wasn't added to Windows when they were forking NT. Being able to put semi-trusted drivers in a separate area, and perhaps even a user session manager too, could allow for some interesting security experiments that don't rely on (para)virtualization.

Hardware-wise, it would be useful to have hardware contexts, like sparcs have, so that the group of registers a process has can be swapped in and out a lot easier. Context switching is expensive, and building processors that realize that the modern user tends to have more than one task running would be a pretty good performance win.