Everything that is free still has to be provided by someone, it has always been that way since the existence of the universe.
Dirt is free and you can turn it into bricks to build a house but you are relying on the existence of the earth and therefore the existence of the universe.
If these comments were followed to their logical conclusion the word free shouldn't exist because nothing can be free. Thanks, now we have to come up with another word for "user doesn't get charged".
People tend to value something more when they pay for it if they work for it. This is why IKEA works. In this line, I think an announcement like "This Saturday your ride is sponsored from your taxes, please enjoy it" would be more fair and would probably do more good in the long term.
Perhaps it would make sense to tackle overly dependence on cars by slapping a tax which is directly used to fund public transport. So the more cars you have registered, the more money goes into public transport so that it can compete better, without getting left behind.
We haven't gotten rid of the word free though. We are now merely fee free.