It doesn't make sense because you don't understand how registered addresses and taxes work in the former eastern bloc. It's common for people to move to a large city and officially still be registered as living at home. Sometimes it's due to laziness, sometimes they don't want to get the paperwork to get registered at their new address, sometimes they just like having mom take care of all their paperwork/tickets/etc.
Free public transportation is incentivizing these people to register where they actually live. They aren't paying more in taxes, they've just registered as official residents of the city, so their taxes are counted as being paid in the city.
It's not just the Eastern Bloc - it's not uncommon in the US, particularly among recent college grads who move to a new state, to not get a new driver's license (which costs $), or to avoid getting new license plates on a car and summarily to avoid the higher insurance costs in that locality, etc..
With respect to auto insurance, the insurance contract is governed by the laws of the state in which the car is registered, however the rate paid is based on where the car is principally garaged. If someone is paying a lower rate by not correctly listing where they live, that is insurance fraud (albeit of the small time variety), and depending on the state can void coverage or incur other penalties.
Free public transportation is incentivizing these people to register where they actually live. They aren't paying more in taxes, they've just registered as official residents of the city, so their taxes are counted as being paid in the city.