I think the broader (meta-?)point of Chesterton's fence is that our beliefs about the reason for the fence can still be wrong because we lost the tacit knowledge that produced and kept the fence there.

So even if the rule shows up in some "city aesthetic code" where they wrote down "yep more than two is ugly", it may very well be satisfying some other desideratum that no one wrote down.

That's not to say this rule really does have other reasons, but you can't stop at "yup that's what our records show". And indeed, some of them mentioned possible safety issues that arise with greater depths.