> How would you then prevent them from re-amalgamating the way Verizon and AT&T did after the Baby Bell breakup? Not just for a few years afterward, but ever?

By continuing to enforce anti-trust legislation, though this time on the opposite M&A end.

> I think that payment processors actually make a pretty convincing natural monopoly

I guess I don't know enough to make an authoritative statement here, but I don't personally find this argument super convincing. I expect the actual breakup would be on the order of like 6-20 companies at most, and it wouldn't be rocket science for some middle-man to abstract out the processing. We solve many harder problems than that in the software industry every day.

But either way, it's a valid argument, and I think a court would be the right place to duke it out. If they are indeed a natural monopoly, then I agree it would be appropriate to start placing limits on their behavior.