> I wonder if that is a factor in folk trying to use it as a vari-mu tube?
You are over-abstracting.
You gotta get down with the electrons. Think like a unit-charge. Feel the peer-pressure.
NO tube has enough range of Mu to give the gain range we need. Vari-Mu is someone's trademark, NOT how it really works.
All tubes (all active devices!) have Gm which falls with current.
Remote-cutoff tubes are optimized for VERY-VERY low Gm at VERY low current. This won't give useful output unless you have a load with small DC resistance and huge AC impedance (radio IF tanks).
What you really want is a tube with modest Gm at fairly HIGH current, so that you still have useful current when you slam the Gm down low.
Also follow plate resistance as tube is slammed-down. If you have a high impedance load, higher than Rp, idle gain is dominated by Rp. As current is reduced, Rp goes up, gain wants to go up. It doesn't; but it doesn't drop much either. There's a trick.
I wasn't aware 12AU7 distortion was notorious. All tubes distort. 12AU7 is often mishandled, and perhaps not real appropriate for general audio. 6SN7 is similar yet more linear, harder to do wrong.
But a small tube's reputation is usually single-ended. A good limiter must be push-pull to cancel thump. The curve in 12AU7 cancels in push-pull... it is a very different device.
And 12AU7's curvature is very helpful in getting a wide range of gain without starving the output. "Good" triodes supress the curve down to low currents. "Hot" triodes goose-up the high-current Gm and let it fall at modest current. (6SN7 is NOT better here; neither are most of the buzz-toobs people think they must try.)