Similarly but not identically, and the top of the curve is what's important
in a switching application where you're trying to saturate the device. You
want something with as abrupt a transition in the curve as you can get, and
something with a huge amount of gain.

You mean, the device needs to be nonlinear?

But you also want something that
switches really, really fast.

Like the 12AF4 or one of the other tubes used in VHF tuners?

Honestly, if you just want the carrier, though, it doesn't buy you anything
over normal Class C operation.

Then why are people putting so much store by class E operation for CW
amplification?

I guess back to the drawing board. What I was thinking was to use a
genny as VFO to
inject a carrier into a buffer amp driving a CW amplifier.