"Back yard" is a figure of speech, just like it is in the acronym. The people of X should determine what happens in X, where X can be <land parcel>, <neighborhood>, <city>, <state> or <nation>. However as you can imagine, there are going to be conflicts between what the people of a larger entity want vs. what the people of a smaller contained entity want. The interests of the people of <state> might conflict with the interests of the people of <land parcel> for example. So it gets murky fast.
I happen to think we should try to err in favor of the smaller entity. Which takes care of a couple of problems: It satisfies property rights as you're saying. And it prevents a small entity from forcing its will on another comparably small entity by appealing to the larger entity that contains them both, which it sounds like you're also concerned about.
But the impact scope needs to be properly defined. Erring in favor of the smaller entity means you define the scope as small as possible. But to remain fair, go no smaller. For one of these towers, the scope of impact is probably <neighborhood>. That's how wide its transmit/receive radius will be (smaller than today's towers), and that's probably also how far you'll have to go until that particular tower isn't visible (which isn't a rational argument by the way, but an aesthetic one, probably lost on anyone born after 1990 and accustomed to seeing shitty towers everywhere).
My point wasn't the merits of any particular argument; I only brought that up to shock someone into realizing people can have contrary opinions, including for no good reason, and if you want to persuade them you have to meet them where they are, just like if you were selling a product to a customer.