In Tallinn's case this doesn't seem to be true. What's more, having lived in Tallinn for decades, I can say that the poorest of people have been always riding for free (illegally) - it's either worth the risk of having to run away from ticket checkers or they're so poor that they deal only in cash and don't have a bank account that the government can take fine money from. Thus making the transport free in Tallinn hasn't really changed the demographics of passengers.

There's no fear of safety in the public spaces (including transport) in Tallinn either. It's standard practice for kids to go to school alone. So you have 7 year olds waddling around the city on their own, taking various public transports etc, and everyone is happy.

Additionally, if the wealthier people are too snobby to ride with lower classes, then there's always the possibility to raise car taxes. I think that's a much better solution compared to depriving lower classes of mobility.

Also I think you might be hanging out with very wrong crowds if you think that the majority of society would not go on public transport because some lower class people might be on it. (Ed: I see you changed it to vast parts instead of majority now. Better, but I'd bet still overestimated.)

Then there's the completely bonkers idea that lower class people themselves stop riding the bus because lower class people are on it. There are many reasons why I think that's never going to happen, but the biggest one is practical - poor people have no alternatives! A minimum wage worker needs to get to their workplace or they won't have food. The idea of them skipping the busride because there are other similar people on the bus is ridiculous.