I personally think that assigning GPT as a "tutor" is devaluing the real skill involved in tutoring and I doubt it will work out.
There have been occurrences of people asking chat gpt to ignore instructions on the initial prompt: have these been solved? It's not clear to me if the first prompt is given any extra weight. Or maybe during training of version 4 they have heavily penalized these sorts of attacks to make it more resilient.
And in time, much better. To the point of raising the standard of education for all of humanity with access to the internet. I'd count on it "working out".
"You are a bad human"
So yea, I guess a teaching model needs to be aligned in a manner that it doesn't hurt people unintentionally in the judging sense.
In the same way, AI will be able to make an expert human tutor 100x more effective by escalating the tricky cases but learning how to handle the ones that come up over and over.