A BJT-based CPU would probably require a refrigeration system to keep it sufficiently cool at just 50 MIPS.
Are there examples of non-CMOS CPUs that were commercially produced?
CPUs on an IC? Yes, HP made a series of machines with Silicon on sapphire substrates, for lower parasitic capacitance.
Under a microscope, you can see thriugh the chip like glass. I don't know what the circuit topolgy was.
IBM made the 370 series with the bipolar junction transistor technology they called MST4, which was essentially similar to Motorola's ECL.
The original Z-80 was implemented in XMOS, I think.
Jon
Quite a few of the early 8 bit CPUs (8080, 6502, Z80) were either NMOS or PMOS. There was also a mix with MOSFETs and BJTs. They later switched to CMOS for lower power and better performance, though it needs a more complicated process.
Somewhat later there was even some ECL type CPU on a chip, to get a high clock speed. At least in the early days, when running at high clock speed the power consumption for CMOS was not that much better than ECL. It only improved with reduced feature size. WIth BJTs it gets increasingly more difficult to make them very small. The main advantage in power consumption with CMOS comes in the idle state or logic in a static state, like much of memory.
Silicon on saphire is just a different substrate, but the process on top could still be CMOS, but also others.
Some of the inventions / discoveries just have there time to come. If it does not happen in one lab, it will come somehere else. Some parts even got invented multiple times - so reinventing the wheel is nothing new.