> A cathode biased power section DOES use a bypass cap, ... Why?
Follow what HBP wrote: "IF the differential inputs signals are equal and opposite, ..., then the signal currents ...offset each other."
Maybe not the full story. There's an input range, for amp-triodes say zero to -3V. Gain stages are usually worked within this range. POWER stages often push past the cutoff. When one 6V6 grid is driven to -35v to -40V, it is practically an open circuit, isn't equal-but-opposite, isn't "offsetting" the other 6V6.
But cathode caps on power stages are a very complicated issue. Analysis is dubious and does not tell "how it sounds". There are many ways to build, use, and abuse cathode bias power stages. The best path is to try no, 10uDf, 50uFd, and 500uFd, over all the clean and overload outputs you may want to play, and hear how it sounds.
Several popular old amp use no bypass. These may be the ones working at lower voltage (250V on 6V6) and thus such high current that cutoff isn't happening often. (It also saved a buck, and a failure-prone part.) High voltage high fidelity cathode-bias amps will probably want a very large cap, 500uFd or so. Guitar amps often have a cap which gives a short hold-up, down near 25uFd-50uFd, and surely selected by ear.