At my kyokushin karate dojo, one of the instructors is nearly 80. He's physically incapable of performing most of the techniques he teaches. Like, one of his knees doesn't really bend anymore, so he can't even kick at all. But he still knows what a proper kick should look like. And he was an actual school teacher for ~50 years, so he's very good at explaining stuff. But he never competed himself. Nevertheless, he'll spot minute mistakes in your technique, then figure out a way to make it intelligible to you, and finally guide you into the correct way to perform it. All while being unable to actually perform the technique himself. He's a wizard, basically.
We have another instructor who is younger, and who used to be a very serious national-level competitor. His physical ability and general martial arts skills are superior to those of the 80 years-old instructor (don't get me wrong, the older instructor is still very skilled, just much older and now physically frail). But students are often at a loss when training under him, because his go-to strategy to correct their mistakes is to flawlessly execute the technique in front of them after saying "No, no! You need to do it like this!"
Despite being able to demonstrate stuff at a very high-level, he lacks the ability to properly transmit his knowledge. He's basically Superman, but can't understand that you're not superhuman yourself. So unless you are yourself at a very high level, or at least at a high enough level that you can easily spot by yourself what makes his technique better than yours, learning under this instructor is much harder. In my experience, thus, being good at martial arts doesn't necessarily make you good at teaching martial arts.
Assuming both of these instructors taught at different schools and you went on to test them with a trial fight as you suggested, you'd probably pick Superman. And I'd say you were missing out, as the Wizard has trained many full-contact karate champions beyond his own abilities, including Superman himself.
I guess what I'm saying is that you're approaching this problem from the wrong angle. Instead of figuring out a way to test instructors to know which is the best individual martial artist, you should be trying to figure out which instructor will be the best at unlocking their students' potential at a given point in time. In my previous examples, the best way to success would probably be to start training under Wizard, then "graduate" to Superman once you've reached a certain skill level. You'd reach the same potential, just faster than starting straight under Superman.