There are tww outputs, one to the plate, and the other to the load( our amplifier, and small resistor next to the mute switch in the schematic ). Since these loads will consume AC, the current delivered to the CCS will be our regulated amount + {load consumption}. The PS is going to have to deliver what is consumed by the load as ideally as is possible. The CCS will act to isolate the triode from this, but it *WON'T* be ideal. So, the better the PS can deal with a slightly variable load, the better our voltage amp will perform.

It is a small 'expense' IMO, but an audibly significant one I suspect.
regards,
Douglas