For one thing, it greatly reduces costs because you don't need all the ticket printing/selling/checking equipment and salaries for all those people who collect the money. You also don't need cops checking people's tickets. Because of this the cost for tax-supported free public transit would be much less than the total cost paid by ticket purchasers currently.
It also greatly improves efficiency because buses can just pick people up without the big stall for ticket buying and checking at the entry way. You can change your buses to have more doors and wider doors so that people can just flow on and off more easily and eliminate the huge pinch point that causes big slowdowns.
This will only appeal to liberals, but it's a nice way of giving back to the working poor. Most people who take the bus to work are working poor and can use every break they can get. Riding the bus will always be unpleasant so it's not like people will abuse the priviledge.
Now some people would argue that free public transit would overburden the system, there wouldn't be enough buses, they would get too crowded. That's completely retarded, that's exactly the outcome you *want*. You buy more buses!
I believe it may actually be cheaper in the long run. If you have more people on public transit you don't have to spend as much making new roads everywhere, people buy fewer cars saving them tons of money, we pollute less and have to spend less on reducing CO2, etc. there are tons of long term savings that are hard to quantify.
Now I'm sure the libertarian/republican/dickhead/ayn-randers out there are saying "but I don't ride the bus, why should I pay for it?" First of all, fuck you, you're a dick. Public policy should be optimized to maximize the total good (or perhaps to maximize the median good), the principle of "pay per use" does not enter into rational consideration of public policy at all. Second of all, *you* are the person who would get the most benefit from this. Personally I would probably keep driving because I hate the bus, but I would love to see free public transit, because it gets cars off the road and reduces traffic for me. It's win-win for everyone.