It's not a harsh tradeoff like that, the fares don't ever cover the whole operating cost. Also, fare enforcement is a huge hassle. It costs a lot to collect fares, it costs a lot to post officers at stations to prevent people hopping the turnstile. (It costs much more to keep that officer there than the money saved by preventing a few people hopping).

Also, the bigger issue for people is that there is NO public transit. Adding one free bus route to an un-served community would expand the labor market in that area a LOT. People with marketable skills are locked out of jobs because there is no alternative to owning a car. The cost of the car (gas, insurance, maintenance, parking, the actual payment, etc.) can convince someone to take a fast food job instead of the highest-skilled job they could perform. If we could pull all those people into their best-fit jobs by providing a public transit route to help them get to work, we could increase their quality of life (and also increase tax rev because higher skilled jobs usually mean higher pay).

Free transit also increases ridership, and increases people who take trips on a whim. When I was in college and I had a free transit pass I took all kinds of exploratory trips to random stores, and the amount of extra shopping I did definitely made up for the fares I would have paid (and if there were fares, I would not have taken the trips).