What is the difference in the end between say using a DN2540 style CCS at the anode vs a LM317 CCS at the cathode? Isn't the end-game objective the same to fix the DC current? Does the anode CCS also provide a higher impedance load benefit, whereby the cathode CCS would only fix the current but not ease the load? What if my driver stage currently uses an interstage transformer load, could adding a CCS above anode choke really improve things beyond a choke alone? Basically if you had a driver stage that had a interstage anode and cathode resistor. And you wanted to add a CCS, would you add it at the cathode or anode?
A CCS in series with an interstage transformer primary will set the average DC current. However, unless you add a capacitor across the CCs, all of the signal voltage will be across the CCS, and no signal across the interstage primary; so no signal on the secondary. Most tubes have reasonably constant average current when you use a self bias cathode resistor. But you need a capacitor across that resistor, or the tube rp increases, and the gain decreases. A CCS in the cathode needs a bypass capacitor, or the rp and lower gain effects are worse than with a self bias cathode resistor.
It's not that simple. A CCS can establish a desired quiescent operating point by fixing the DC current, but it's real purpose is to establish a high AC resistance to signal currents. Whether that is advantageous in the plate circuit or the cathode circuit depends on the application. That's the important take-away here.
As an example, in a common cathode gain stage, the gain is approximately equal to the transconductance (gm) of the tube multiplied by the dynamic resistance of the external plate resistance in parallel with the tube's internal plate resistance. So in this application, a CCS in the plate circuit will greatly increase the stage gain, approaching the amplification factor (mu) of the tube.
In a differential amplifier configuration like a long-tailed phase splitter, balance between the two tube sections will be improved by using a higher value cathode resistor. But using a large fixed resistor often requires a high negative voltage power supply in the tail circuit to set the proper DC operating conditions. So a CCS in place of a fixed cathode resistor provides the large dynamic resistance that the circuit likes to see without the high voltage DC bias supply.
In short, it's important to understand the difference between the DC operating conditions and the AC (signal handling) behavior. A little circuit theory study would be helpful here.