I sent the author an email about horses and reins and stuff.
In other news, I held off watering my trees and got free rain all night. But I doubt we’ll ever be rid of “free reign.”
The problem is that “free reign” seems to make sense, as in to reign freely, until you think about it a little, and compare it to the idea of giving a horse “free rein”. Unfortunately, most people don’t think at all about the expressions they use, so you’re right: “free reign” will not go away.