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Yes, but for the previous few generations of transistor manufacturing, transistors' power consumption has not scaled down as well as their size. This is known as the failure of Dennard Scaling[0].

[0] https://en.wikipedia.org/wiki/Dennard_scaling

Power leakage is an increasingly large problem nowadays. (Because yes, semiconductors are nowadays suffering from observable quantum effects.)

Yeah but power consumption increases with something like the 4th power (heh) of frequency so there's not much you can do even with really low power transistors.

According to this article on Wikipedia, it's a linear relationship: https://en.wikipedia.org/wiki/CPU_power_dissipation

Edit: maybe this takes into account that when you increase frequency you might also have to increase the voltage to keep the processor stable, as well? But a 4th power effect seems quite extreme.

Yes, but just like Moore's law is on the edge of being mined out of the easy gains, so is Dennard scaling.