I hear you yell. No, it won't. Even a high impedance 12AX7 plate is not affected in the audio range by this capacitance. I have done this, and what's more, done the necessary measurements to find the effect on the response of the composite stage - and there is no detectable change in frequency response below 30kHz. This squares with the empirical evidence of listening to it - it sounds the same as when a triode is used as a cathode follower.
Some amps use the triode cathode follower to generate distortion.
When output tubes are overdriven, their grids are often driven positive. So on overdriven notes, the output tubes are pushed into a harsh-sounding crossover distortion. This clipping can be as harsh as any solid state situation. The solution to the class B bias shift and grid current clipping is to drive the output tube grids direct coupled from a cathode follower. This means that the cathode resistor is tied to a more negative voltage of something more than twice the bias voltage, so it can pull the output tube grid negative.