> We could just lower the cap value to reduce the current requirement, couldn't we?
Yes, but maximum release time would be shorter.
We could increase the size of the release resistor, but grid-current is only "small", not "zero", and a very-large release resistor times +/- stray grid current = uncertain grid voltage. As an extreme, a transformer-loaded stage as in Fairchild "could" go run-away and melt.
And Fairchild has multiple grids in parallel, more grid current.
Instead of grid current, tubes are often rated for a maximum grid resistor. OTOO 1Meg. Fairchild has four grids, 1Meg/4= 220K standard value.
So in the simple case, the maximum safe grid resistor, divided by the ratio of max release-time to min attack-time, sets your attack "resistor", including amplifier and rectifier resistances.
And the maximum control voltage, divided by attack resistor, is your peak charge current.
My tubes are rated 1Meg max grid resistor, I have two, my max grid resistor is 500K; this is also typically my release resistor.
Say I want 0.5mS attack and 5 Sec release, 10,000:1 ratio.
The attack "resistor" is 500K/10,000 or 50 ohms.
Say I need 25V control voltage swing. I need 25V/50R= 0.5 Amperes, at 25V, is 12.5 Watts peak. I need at-least 6.26 Watts Sine RMS amplifier.
The Fairchild has a faster attack, even more grids to drive, and low-Mu tubes working at good high voltage, needs like 40V of control voltage. Hence the 15W Sine RMS sidechain hammer.
Yes, buffering a hi-R time-constant network to the tubes would allow less heroic hammer. 13-cent TL072 would allow 1/10th of the sidechain amplifier power, IF (as you say) it can swing the control voltage (the Fairchild's CV is beyond the reach of cheap chips). Or you could derive a 0-4V voltage on the cap, then amplify it up to 0-40V. And you will have more/less trouble with leakage around hi-Z networks; the 99-cent cheap phenolic switches may show faster release on very humid days.
Does it make the music better? I don't see much need for attacks faster than a millisecond except as the final stage before an "Oh, CRAP!" recorder where the slightest overload will ruin a take. Tape don't mind overload. Digi-systems should clip without distress. The primary need for a fast limiter may be phonodisc cutting, because if grooves touch the master is useless.