Yes, the definition of linearity is that f(A) + f(B) = f(A+B), which you have contradicted in your GP post. If a transistor is fully on, then doubling the input voltage to it will not double the output, because it's already at maximum. That is very precisely not a linear device. That's why linear amplifiers, like Class A, operate the transistor in a partially switched state, where increasing the input signal (about some bias point, and with feedback to turn a real transistor into a more ideally-behaving one) gives a corresponding increase in output signal.
Class D (switching) amplifiers are _not_ linear, they trade linearity for efficiency. The article you linked to actually says this:
"Over the years, a number of different biasing schemes have been developed for amplifiers, from extremely linear Class A operation, in which the active devices essentially remain powered on through the full sinewave cycle of an input signal, to more power-efficient schemes, such as Class D, in which multiple transistors are switched on and off to conduct different portions of an input waveform."
I think what you are doing is confusing the linearity of the transistor with the linearity of the whole audio amplifier treated as a black box, which is why I suggested you rephrase your argument rather than say you are categorically wrong, however what you said was:
"The thing is that transistors’ behavior is more linear and controlled when fully on or off rather than when used as continuously variable."
... which I'm afraid is really just wrong.