The difference between a Barkhausen-Kurz tube and a transmitting triode

It's (capacitively coupled)negative feedback so the gain is controlled about 66K/1K = 66.

The feedback is applied to the cathode of V1a rather than the grid because it needs to be negative feedback.

One specific datapoint : some years ago I made some measurements on a 12 watt valve amplifier (Leak TL/12+) it met its rated distortion specification (0.1%) at 12W rms (at 1kHz).

However, by the time distortion reached 1% it was generating 20W rms, while most transistor amplifiers would have started clipping immediately beyond its rated power.

I stopped there and didn't find out where it reached hard clipping or even 10% thd.

(At high levels, very little of that distortion was 2nd harmonic, thanks to the push-pull output stage)

As for why : with transistors, it is easy to add gain and thus employ more negative feedback, and the emitter followers typically used in the output stage are relatively linear; so it is easy to maintain linearity right up to the point where the output hits the supply rails.

With a valve amplifier, additional gain stages are expensive, so you have to meet your linearity target with relatively little negative feedback. That means designing the hardest bit - the output stage - to be reasonably linear across as much of its range as possible, and restricting the rated power to that range. There are tricks to increase that linear range somewhat, such as connecting the screen grid to an intermediate tap on the output transformer, somewhere between V+ (pentode connection) and anode (triode connection) - tap at 43% for the so-called "ultra-linear" connection.

Beyond that range it will still amplify, and produce additional power, but no longer meet its distortion specification, up to some limit where real clipping will occur. Triode-connected gives the smallest linear range (therefore the lowest rated power) but, by the same token, offers the largest reserve of power in overload.