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.