Some of the later generations of autobias overcame that issue. Take a look at the designs from Morgan Jones and Menno Vanderveen. I’ve used Morgan’s circuit, and it does what it says on the tin.One issue with auto bias, which was recognised even in the 1950s, is that a class AB1 output valve can be biased either for continuous sine wave or speech and music duties. Distortion will be very different under the two conditions. The reason is that with speech and music (assuming reasonable dynamic range) the average current drawn by the valve is low, close to its quiescent bias level. With continuous tone, the current draw is much higher, and so the bias voltage will rise due to the bias being derived by the current through the cathode resistor. An amplifier designed for sine-wave duty will have the wrong bias (too low) on speech and music, and one designed for speech and music will have too much bias on tones. That makes it difficult to measure distortion accurately, although manufacturers who understood this at the time, would create a fixed bias so the amp could be measured. The cathode bypass capacitor created a long(ish) time constant that smoothed out the bias variations on speech and music, but that wouldn't work for tone which by its nature is continuous.
High power valve amps typically had fixed bias using a separate supply that didn't have the issue with bias shifting with signal, but this added considerably to cost so wasn't used on most lower powered amps.
S.
Of course, one of the classics was the early digital autobias in the Audionics BA150 from the late 1970s.