I took your advice and looked at some financials. The total revenue/cost of revenue for Visa in their most recent info was 5.5. That does seem like a more than healthy profit margin.
For context, here is the same ratio for the FAANG companies and a few telecoms. I would've included some banks as well but they report their income differently so I didn't see an easy way to calculate the same ratio.
Facebook 5.5
Amazon 1.3
Apple 1.6
Netflix 1.6
Google 2.2
AT&T 2.2
Verizon 2.4
Comcast 3.2
Out of all these companies the only one with a better ratio was Facebook. However, if you look at total revenue Visa was by far the smallest of the companies I've listed. Based on this info I can agree that Visa could reduce their fees and still have healthy profit margins. If you want to use this as evidence they charge too much and need some form of government intervention you might want to look at Facebook first and keep an eye on the cable companies.