The cathode bias resistor and plate loading resistor create intersecting lines on the tube curves to fix an operating point. With a resistor used for plate loading and biasing, there's strong DC feedback and you get very reliable plate voltage coming out. On the downside, you will lose gain across the cathode bypass resistor unless you use a capacitor across it, and that capacitor has to be chosen correctly so you don't get any response loss from the shelving filter formed. The quality of this cap can also become important when the signal levels are very small. If you substitute an LED for the biasing resistor, the circuit will operate as though there's a near-perfect cathode bypass cap with the downside that the plate voltage value will tend to wander a little more than it otherwise should.
It is important to keep in mind that not only do the LEDs we provide sound better than any RC combo we have tried, but they also cost a little more.