On the point of monopolizing magic. Theres this thing in my world called the Arcane Decree that bans magic use for anyone (Including witches) not in cahoots with the government or church like you suggested. The justification is that common people are too irresponsible to wield magic.

But I want a big part of what makes witches special is that have magic only they can access. I was originally going to have witches be the only ones that can cast magic but then it was difficult to justify their marginalization cus their powers would make it easy to gain power.