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In the few textbooks I'm reading on CMOS analog design, they all seem to have reference currents of \$10 \mu A\$ or similar that get mirrored, and there doesn't seem to be any discussion on how this reference value was arrived at.
Is there any science to choosing these bias current numbers? Why is it not \$1\mu A\$, or \$200nA\$ or something to save power?
First of all, bias currents in the range of 1uA or below are used as well. It's just not that common.
The current in a circuit is determined by a number of factors, like bandwidth and noise. This results in typical currents that are in the range of a few uA up to a few mA. These currents need to be derived from a reference current and having the reference current in a similar range makes this task easier.
Deriving 100uA from 200nA would mean a scaling factor of 500. This is impractical because such a ratio introduces larger variations due to mismatch. And there is usually no point in saving 1uA when the circuit needs a few hundred uA.
Regarding mismatch in a current mirror it is also important to minimize the transconductance to current ratio of the transistor. To this end for MOS transistors a minimum current is required, to get a sufficiently high overdrive voltage.
The simple answer is NOISE tradeoff. Noise issues are typically forgotten in digital circuit design, (because the signal-to-noise ratio is sufficiently high) but when they matter (e.g. high gain amplifiers) they matter a lot.
In a MOSFET, two primary sources of noise are thermal noise in the channel and flicker noise. To this day nobody really fully understands where flicker noise (pink noise) comes from, but fortunately we can measure and model it.
When noise voltages and noise currents become near equal in size to the operating voltages and currents, they cause havoc in your circuit, because their behavior is totally random. Who wants a circuit that does random things? Only cryptographers...
Miminizing noise is a complex art, but in typical circuits, it turns out that total noise is usually inversely proportional to current, and proportional to bandwidth.
Therefore, the designer picks a (bias) current that is as low as possible (to save power) but high enough to meet the required signal-to-noise and bandwidth behaviors of the application.
