Quick recap: actually, vacuum tubes are far from saturation when set to normal bias points. Look at a 300B, or any other power tube. Normal quiescent bias is set between 60 and 85 mA, if Class A operation is desired. If Class AB is desired, 35 to 40 mA is more typical. With 400 volts from cathode (or filament), that's a steady-state plate dissipation between 14 and 34 watts, well within the 40-watt rating.
But that's nowhere close to the peak current emission of the cathode. I've measured 250 mA from a generic 300B, and the exotic European 300B's can slam out nearly 500 mA (transient). The only time I've ever seen a 300B current-limit around 80 mA were some particularly weak Chinese tubes from the mid-Eighties ... they sounded and measured pretty bad, and were near-defective. Other vacuum tubes are similar; the recommended quiescent currents are set by plate dissipation limits, not cathode emission maximums (which are left unspecified). Transistors will melt the internal copper links, but damaging the cathode in a vacuum tube is really hard to do unless the tube is operated with no B+ present.
It's transistors that have Safe Operating Area (SOA) curves that are log-log in both current and voltage (with an additional time dimension), not tubes. The current saturation mechanisms are totally different and have nothing in common.
Unlike transistors, vacuum tubes have very large areas of peak current emission that are left untapped by most circuits. Of course, plate heating goes up when these areas are explored, but unlike transistors, tubes do not fail in milliseconds (this is shown in the SOA curves of transistors, and must be respected). It takes sustained abuse, over many seconds, before mechanical deformation dooms the plate.
I think Ralph will agree that Class AB operation is not "false". In Class AB, one device cuts off (goes to infinite impedance and conducts no current) while the opposing device goes to a large multiple of the quiescent current. In conventional Class AB transistor amps, the idling current is a tiny fraction of the peak current, and in Class AB tube amps, it's still a small fraction.
Let's look at what happens in pure differential circuit, either tube or transistor, with a current source setting the quiescent current. This circuit must always operate in Class A. Unless something fails, the current source will always deliver the programmed current ... that is a hard limit that cannot be exceeded under any condition.
The late Allen Wright actually built a PP 300B power amplifier that had a current source under the pair of VV52B's (massive Czech power tubes). He stayed at my house during one of the VSAC shows, and we compared his amp to my early version of the Karna (which has bypassed cathodes and can operate in Class A, Class A2, or Class AB, or even Class AB2, depending on current demand). Allen's output stage was true differential, and true Class A, with a powerful solid-state current source running around 160 mA (if memory serves ... this was in 2003 or so).
The two amps sounded completely different. That's when Allen, and I, realized that differential, and balanced, are not in fact the same. This is a common illusion, a hangover from the Fifties. The question is what happens when one device cuts off.
When this happens in a current-sourced differential circuit, the "ON" device can never pass more than the total current programmed in the current source (by definition). That's a hard limit. It is a brick wall. The circuit, as a whole, will always pass whatever the current source is programmed to do ... no more, no less, always the same. This is why this circuit is seen in the Mullard topology as a low-power, medium-voltage phase splitter. Allen, as a big fan of differential circuits in Tek scopes, took it all the way and used it in a power stage.
This is quite different than a Class AB, or conventional Class A, power stage. Whether cathode or fixed-bias, current flow through the output pair is dynamic. IF (a very big if here) the output tubes were distortionless, perfectly matched, AND never voltage-clipped or driven into Class AB, yes, it would behave the same as a current-sourced pure differential stage. Only then are they the same.
But we don't live in a world of Platonic ideals. Tubes are not actually the same as the tube models, they are not perfectly assembled in perfect factories by robots, loudspeakers have odd ideas when they want lots of current, and bass drivers in particular are notorious for nonlinearity and very long energy storage .., all of which affects output stages.
So a power amplifier must deal with speakers as they are, not as we want them to be. So peak current excursions can be accommodated when necessary, without the amplifier grossly departing from basic design assumptions. The loudspeaker conforms to Theile/Small equations most of the time, but both Neville Theile and Richard Small warn us that these are only small-signal approximations. They are not valid once the voice coils start to move significantly. Speakers are only linear on average, not all the time.
My goal with Class A output is to synthesize a fixed output impedance that remains constant with real-world loudspeakers, which I have been designing since 1975. I know how awful speakers are. Most power amps use 20 to 50 dB of feedback to synthesize a perfect voltage source, and they do a pretty decent job of it. With zero feedback, the best I can hope for is a fixed, moderate-value equivalent resistor, about 2 ohms or so, which a low-Q vented or closed box speaker can deal with. And an output stage that does not have a hard current limit, but soft-clips in both voltage and current, without requiring protection circuits.