I can see that leading to a civil war among the wizards. The White Council will never go for an open school headed by Harry, they will want his head more than ever.
I think it'd be
very complicated.
To begin with, I don't think there are enough "pro-Harry" wizards to support a civil war, as such.
A "war" against Harry, or his "school"?
I'm pretty sure the White Council wouldn't go to war against
Winter. Frankly, that would be tantamount to suicide, and I think most of them know it. Harry's the WK, and with winterfae now inhabiting the Castle, it would be hard to see a White Council attack there as anything else.
I have posited the same.
The Paranet know what the WC have done to Harry despite what Harry did for the WC, they are not going to pass potential Wizards to the WC they are going to pass them to Harry. That’s most of North America.
Harry is also going to be a magnet for disaffected and abused apprentices from the WC from across the world, and wobetide the Wizard who so abuses his young apprentice that they reach Harry. They will be so forced to swear on their power that they will not be able to do anything.That’s a smattering of apprentices across the world.
Harry can’t do one on one teaching in these circumstances but could engage others, Elaine and Molly and Mort (for Ectomancy directly, but no reason he can’t channel say Morgan for evocation and Mort could stand to broaden his education), Butters for magical theory and comparative supernatural biology. Guest Lecturers like River Shoulders or Kringle. If he can save Chandler in Mirror Mirror, then he has another teacher who would be delighted to teach. Harry doesn’t have the WC prejudice against non-human practitioners.
My own theory is that the Paranet itself will become the "school." I'm sure they count some talented educators among their number, who could design curricula. I would think of Harry as more in that "guest lecturer" role...
... specifically, teaching
Defense Against The Dark Arts!
But the Paranet can teach many students the introductory material, only calling upon the stronger practitioners for specific "special needs."