> I don't know if this translates to low power audio use
Not very well.
Any loose atoms inside the tube become positive ions and slam into the cathode with enough force to cause damage.
Below 500V, we can use Oxide Cathode, which is a soft "frosting" which emits electrons VERY easily, and has no hard limit on emission. The 15mA/Watt guide can be exceeded without great loss of life. But plate voltages over around 500V or 1000V average will bombard the cathode and destroy it.
Up to 5,000V (your 4CX15000 says 10KV), we can use Thoriated Tungsten. Tungsten wire doped with thorium; when hot, the thorium is a monatomic film of liquid clinging to the tungsten. Emission is much lower, which means higher heater power for similar current, but the thorium film is self-healing to a degree so it will stand hard bombardment. To get good performance, the filament temperature must be closely controlled: too hot and the tungsten and thorium evaporate, somewhat cooler and emission falls to useless levels.
You were able to trim-down the heat because your specific application did not need the full 5 Amp rating, or the 5A rating was conservative. And actually, your 6.1V is within specs for 4CX15000.
The performance and trade-off are quite different, Oxide versus Thoriated. You just can't quick-kill Oxide, and it is hard to find emission-limited conditions. OTOH, Thoriated emission sags quickly as heat is lowered, and going much lower may kill it quick. When run "right", life really is limited by cathode wear-out... that's very uncommon in little oxide-cathode tubes which usually go gassy or have a melt-down accident long before the oxide is used-up.
At even higher voltages we must use plain tungsten, which has to be run just under melting-point to be much good; heat is very critical.
For lurkers: 4CX15000 suggested conditions are 10,000V plate supply, 4.55 Amperes cathode current. You are supposed to give the filament 6.3V +/-0.3V at 164 Amperes. In FM service this gives 36,000 watts output, 9,000 Watts plate dissipation. While the 1,033 Watt filament seems like a lot of power, the ratio of filament power to output power is very much better than puny-volted 6L6 etc.