... Great explanation HBP. ...
I actually dropped the ball, twice. Called LooseChange by the wrong name (before edit), and also forget to prove why deep class AB is hard to do with a cathode resistor.
So I think we understand class A is easy to cathode bias, because the average tube current doesn't change much. Let's go to the other extreme: textbook-definition class B.
According to the definition, in class B the tube passes current for exactly 50% of the input signal cycle (class A is 100%, class AB is >50 but <100%). To do this exactly in accordance with the definition, you bias you tube right at the point plate current cuts off. That way, the whole positive signal cycle causes plate current to flow, while the tube is cut off for the negative half-cycle. Obviously, the other side of the push-pull output picks up the slack.
But Voltage = Resistance *
Current. If there is no tube current, there is no bias voltage across the cathode resistor.
"But wait!" you say. "I could use a really huge resistor to bias the tube on
just a little and be close enough, right?"
Sure, and that's how tubes are generally biased to class B, but not with a resistor. The problem is the bias-shift Seedlings mentioned. This isn't a big deal in class A, where a theoretical perfect device has the exact same idle and average current. Real devices have increased screen current under driven conditions, as well as an apparent increase of d.c. due to tube distortion. As you progress from class A to class B, the ratio of average signal current to idle current keeps increasing; theoretical class B would go from 0mA idle to few-hundred mA peak.
You'd need a big cap to fake fixed-bias with your BIG cathode resistor to make our class B stage. What happens when a BIG transient hits? The BIG cap is need to source the big current for that transient (to effectively bypass the big resistor). Once the current is drained, other high-level signals cause the resistor to have a bigger voltage drop, turning the tube more-off.
If low-level signals follow, the tube stays cut off. That's because the big cap value and big resistor lead to a long time constant, so it takes longer for the cap to settle back to the proper bias voltage. At an extreme, you could have each side of the push-pull cut off except for the very peaks of the input signal, so the majority of the input is chopped out. This would be "crossover distortion" to a pretty extreme level; the output would be biased into class C (works great for RF transmitters, not good for audio, which is probably why most readers won't know what it is).
So that's an extreme limit case, but it serves to explain why cathode bias works great for class A, can work good for stages straying lightly into class AB, but isn't used for deep class AB (or B) stages trying to get big output power from the tubes.