Please notice that I didn't say the black deposit is caused by high current, I just said I expect a certain influence.
If the tube specification doesn't require a series inductor, you can assume direct connection to a standard (non-electrolyte) capacitor as intended operation. In this case, peak current and pulse duration are only set by the tube characteristic, anode voltage and capacitance. Regular capacitor ESL and circuit stray inductance won't have a significant influence on the current waveform.
In other words, the life time expectation in the datasheet is assuming a standard circuit and operation conditions without waveshaping means.