They could have used eurodollars but as you note it all began long ago and nobody could be bothered to change. And these fixings were not even far from whatever rate was believed to be their true rate ((for how much and from who? Always left out). Why anybody would use it in swaps was crazy. And the fx fix outlived its usefulness in the early 80s yet some clients still insisted on using it.

The flip side of libor is the rage against spoofing. As long as the price is available to be dealt on for some minimum time, who cares? You think its wrong then go deal on it. In the days when fx and money/bond markets were not totally automated trading was all about psychology- which side would cave first. Pushing prices and then calling off the weak side was just good market making.