Mosfet contradiction?
Actually the main reason why almost all logic is made in CMOS (NMOSFETs and PMOSFETs) these days is that CMOS logic in chips (and almost all logic is in chips) scales down much (can be made smaller in size) much better than BJTs.

Have you heard of Moore's law ? Well, this "law" today almost exclusively applies to CMOS logic using MOSFETs. In the 1970s BJT logic could still scale down in size so then it did follow Moore's law. But it was soon caught up by CMOS which results in much smaller power consumption (especially when the logic is static, meaning not doing anything) and when CMOS became more advanced, higher speed also.

Today's smartphones would be impossible to make using BJT logic as the phone would be as large as a refrigerator and it would need a battery of equal size.

"below 10V, they will act like resistors and generate lots of heat"

That is complete nonsense. Forget that, you must have misunderstood that because it is untrue. Today's Intel CPUs use CMOS logic running on 1 Volt or less. These transistors are damaged by only 2 Volts at their gate.

Also behaving as a resistor does not imply that heat is generated. Only if current flows heat is generated. In CMOS logic the main source of power dissipation is caused by the charging and discharging of the gate capacitances.

"mosfet can have noise at the gate"

I also think you misunderstood this statement. 

All devices generate noise including BJTs. For logic circuits, noise (I'm talking about flicker noise and thermal noise) is generally not a problem since the signals (even when using a 1 V power supply) are significantly larger than the noise. Noise is only an issue in analog designs, not in digital. Noise or better: disturbances on the power supply is an issue also in digital and that is why a lot of supply decoupling (using capacitors) is needed.