Not quite. The private subway companies signed contracts in 1913 fixing the rates at 5 cents. Then WW1 started and caused inflation. The private rail lines put themselves out of business by agreeing to a deal they couldn't uphold. That's capitalism baby!
You are right that I support free fares because it doesn't make that much anyway. The cost or charging includes the digital pay system management contract of the OMNY system, the purchase and maintenance contract for the turnstiles themselves, the pay and benefits costs of MTA employees and police stationed at each stop to prevent fare jumpers, the cost of trial and potential jail for fare jumpers, and probably other ancillary costs associated with charging fares.I can't begin to calculate these costs. How would I even calculate the cost of something more esoteric like the environmental cost of the people who drive that would instead take the train if it were free?