The warm-up on GZ34s is slow enough that most small (B9A) valves would be faster. So if the regulation on the mains transformer isn't great then using a thermionic rectifier could make the difference between over-volting the reservoir and HT rail smoothing capacitors or not. What voltage drop there is also helps with limiting the size of the charging current pulse on each half-cycle. This can be a noise issue in audio gear as well as limiting the strain on the transformer. Of course in the event of a swap to solid state there's nothing to stop a resistor being put in series with the silicon diode.
And if we want to go the whole hog then we could replace all the valves with nice big FETs
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Cheers,
GJ