What bearing does the dollar have on any of this exactly?

What do you mean? How it cannot? In Europe's context, 60's and 70's, was a collection of fractured dozens of small countries each with its own currency. US had a single currency which was also world's reserve currency so every major bank on this planet already had to build technical and legal pipelines to handle global trade. On top of that you had US omnipresence in post WW2 Europe and world for that matter. American payment networks were the fastest and obvious place to build payment networks across all those borders which was then also a footing ground into intra-market payments. As I said - geopolitics, dollar, network effect in that order. Can't have one without the other.

	▲	lxgr 5 hours ago \| parent [-]
		Banks can settle with Visa and Mastercard in their currency of choice, so I don't see why the dollar matters for any of that. And regarding Visa and Mastercard being US payment networks: This is now undoubtedly the case, but for much of their history, their EU subsidiaries were actually independent cooperatives owned by large European network member banks. They only sold their respective stakes to the US parent organizations in the late 90s, back when European banks, in a pretty severe blunder, considered cards a thing of the past of no importance for the future.