Interesting. I see what you mean. Limiting it to .gov domains would make this hard to do but that cat is out of the bag and, in practice, we're better served with an open bidding process.
However, I did find it painful just now to find who etimspayments.com is since they're using domain privacy even though they are the SF provider https://wmq.etimspayments.com/pbw/include/sanfrancisco/input...
I was just talking to a friend and he put in a CPRA request to find out which LLC provides that service so we'll know soon enough.