Collars are fine if you want to manage them, be able to lead them for hoof trimming, shots, whatever. Ours were for showing at the local fair and state fair. Its leashes that are bad, tying goats out so they can eat. Their throats are very delicate and they are prone to choking. Plus they are so active and can get into trouble.
My niece has collars on most of her goats so she can grab them for milking, or to help her move them around although she really doesn’t need them. The goats love her & follow her like the Pied Piper :-) She bought a Nubian buck last year & it was a two-fer with a Nubian doe. After ‘the boys’ (she had a Dwarf Nigerian buck too) had done their duty, they were off to the livestock sale & the doe went as well. My niece would be leading the herd to a new field & this doe would get half way there, then run to the barn repeatedly & caused all sorts of havoc. She also was not friendly so off she went.
Whups - I discovered I still had this window open!
Anyway, maybe wireless collars (such as for dogs) would be ok, since there is no physical restraint. Then again, maybe goats will behave differently than dogs do, with wireless collars.