Hi,
I think in the field of "hi-end-teaching" we find some teachers whose actual performances we won't find easily, e.g., on YT or elsewhere, for example Prof. Karl-Heinz Kämmerling (+), or Prof. Peter Feuchtwanger, or at least another 1 or 2 ones. But we should note that even they will have had to perform, for example for examination-purposes, in front of their own teachers.
Then, we have, in such cases, to consider that
such teachers always should / will be able to show AT THE PIANO exactly what they mean, for every piece existing, so that the student in any case gets a good imagination and that all her / his questions can be answered.
And such teachers, who mostly teach or have taught students who ARE already very very good, or are teachers themselves, would maneuvre themselves into an unpleasant situation, if one of these accomplished students asked them
"oh, I cannot do that: could you show me, please, by playing it yourself, the final 5 pages of the Liszt-b-minor-sonata, please?"
and then, the teacher cannot play it. That would be unpleasant, and students perhaps would talk about that, and / or leave.
Thus, we can assume, that there are VERY VERY GOOD teachers who rarely or never perform(ed)
in public concerts during their career as a teacher, but could, in spite of that, ALWAYS and in ANY CASE
show their students and ( additionally), give satisfying answers to already very accomplished students.
Secondly, we might notice, that the more mediocre the teacher's "fame" is, and the more unknown his name, the more she / he will have to perform in public concerts, to increase fame and to make her / his name more relevant in the public. (Because otherwise this thread won't have been started.) The second way to become "famous" - in the local view of their cities, of course, where they live, (but not too much more in the "outer conurbation areas" surrounding ) - would be that they are, due to their character or appearing, e.g., extraordinarily popular in the music-school where they teach. -
But for exceptional teachers as 2 of them are mentioned above, as I assume, this isn't necessary, ( since such persons will train themselves automatically by showing things to their students / by teaching, or they train and practice the relevant things, which they themselves evaluate as important, in privacy, to keep or even improve their standards in actual teaching. )
They don't need teachers any longer, and they don't need public performances to increase their fame or influence.
Final case would be a retired teacher of either the first ( exceptionally hi-end ) or second ( mediocre ) proven abilities or proven fame who doesn't perform ANY LONGER in public. This has to be considered, too.
Cordially, 8_octaves