You are right, however if it would have been made free and kept free indefinitely this would have been a one-time cost.
[1] Some of the big cities are actually even closer to break-even as far as day-to-day operating costs are concerned, so in those cases the budget would have to be increased by an even larger factor in percentage terms.
You aren't taking into account the money saved from eliminating all the infrastructure needed for collecting and enforcing the fares like OP mentioned..
Unless farebox recovery ratio already subtracts the money spent to collect fares? That's not my understanding though.
Aside from that, though, it's not as if the money not collected in fares is lost. That's money that people get to keep. It's a direct economic benefit to people using transit, and a smaller indirect benefit to everyone else.