[old_tv_nut]

If the picture is black, and the brightness control has been set so that the CRT draws no current at black, then the diode will not supply any current during the sync pulses, and the cathode voltage will remain at the same voltage as usual.

But, you have pointed out that the CRT is a non-linear load (very non-linear when the current goes to zero), so this results in a variable time-constant for decay of the capacitor voltage, hypothetically infinite if there is no leakage whatsoever. So if this results in odd transient behavior (for example, when the picture suddenly cuts from bright to black or vice-versa), it can be reduced by putting a high value bleed resistor across the diode, just as is done in the grid-drive case.

You have made me realize that in the case I mentioned of a transistor amplifier, it is biased such that the current never goes to zero, so such problems cannot occur.