Bipolar transistors:
on a chip, BJTs can't be made as small as MOSFETs, so any CPU made with BJTs would require an extremely large chip (making it expensive) or on a small chip you would be extremely limited in how many transistors you could use.
cannot be used to make power efficient logic circuits. We used to use TTL logic (based on BJTs) which uses a lot of power compared to CMOS (based on MOSFETs). If the circuitry on your smartphone was made using BJTs only, the phone would be the size of a truck and you would need another truck with a generator to power everything including the cooling system.
The fact that BJTs may have one or a few advantages over MOSFETs doesn't mean that the other huge disadvantages of BJTs for logic circuits suddenly disappear.
You cannot dismiss power and thermals (ad cost!) in this, because those are the reasons that CMOS is used for making processors and not Bipolar technology.