As a broadband customer, I pay for access to "the Internet". Over the last couple of decades, "the Internet" has meant access with something akin to net neutrality in place.
What my ISP wants to sell me is not "the Internet", but something new, which they have yet to define. But from what their lobbyists have put into the FCC proposal, the "Internet" they want to sell me is one where both sender and receiver of data pay them for data. This is not a wholly unreasonable payment model, but it would represent a profound shift in how the Internet is paid for in the U.S.
Further, under their proposal, my speeds to any particular website are dependent on how much I pay and how much the other side pays to my ISP (not theirs). Crucially, half of this is wholly outside my control. Of course, I still pay for the full pipe regardless.
Note that in particular the source server has not been a customer of my ISP, but the FCC thinks they should become a customer of my ISP so that I can have the speeds I have been sold as of today. This is not how the Internet has worked, and is a new service offering being marketed as "the" Internet.
So a better Stripe analogy would be that Stripe offers would be if they 1) first became as big as Chase, Bank of America, Wells Fargo, and American Express combined (that would give them approximately the market heft of the American broadband ISPs); 2) required cardholders to buy a Stripe Consumer subscription before processing their cards for merchants. I'm fairly certain that even our lax banking regulators would have something to say about this.