What if the public transport is free supported by property tax?

We had a discussion a couple of days ago during lunch at the university cafeteria. Discussion was about ticket checking on trams, metro and train. As the economics of crime and punishment suggests, our Dutch colleagues suggested that its fair not to check every passenger for tickets every time but instead to check infrequently but fine heavily those traveling without tickets.
Yes, this is also interesting. The most effective way, as Amatya Sen said, something like, check once a year, get a person and put him/her in death penalty...

Carlos then threw a proposition which wasn't entirely new to me: that public transport should be free and that it should be paid for through property taxes. The argument is that that it would remove the need to put resources for ticketing and ticket checking. But also that it would encourage people to use public transport more than private cars (positive for the environment and in some cases reduce travel time).
The other side of the story might be to encourage more travel demand: people who used to bike, may take the public transport instead. The cost will increase.

Some of us immediately started thinking about free-rider problems...they were quickly dismissed as non-arguments by Carlos. The renters would indirectly pay for their travel through increased rent that they would pay to the landlord to cover for the higher property taxes. The people who live outside the city and commute to the city for work will pay through their employers who rent work space for which property tax is paid. Out of city tourists will pay their part when they shop in the city or visit museums or eat at a local restaurant or stay in a hotel - each of those businesses pay property tax.
I am more convinced with the purpose of cheap or free public transport in for the increasing of available land for cities development. For high density cities with limited land, the development of public transport and make it cheaper, allows living a little further away but on main public transportation corridor attractive.

There will invariably be some free riders - for instance, poorer tourists or backpackers/campers who do not spend enough in the city for its propertied class to justify paying for her/his local travel needs. But lets suppose that the numbers of such free-riders are comparable to the current ticketless travellers who do not get caught. Would this then be a fair system to finance a public transport system? My answer would be "maybe".

First, there will be some who would pay higher property tax even though they don't have much local travel needs - the retired people, for example. It would be a bit unfair for them to have to pay for the travel of those who travel more frequently and those who travel long distances. There will be no monetary incentive for people to pick their location for residence close to their workplace. And there will be boundary problems: people will move right at the edge of the city
just outside the city limits thus avoiding paying higher property taxes but still availing free public transport. (Carlos' response to that one was that this thing would only work if this system is formulated at the metropolitan level, therefore avoiding the boundary problem. Then my next question would be that the metropolitan area also would have a boundary - what would stop me from locating right outside the metropolitan area?)
This reminds me of the public transport fair zones in many cities in Europe. We once traveled in Milano one more stop than our ticket allowed us to go, then it created the trouble on our way back, we couldn't get inside the station. I think there should be studies on whether this zones with different metro fair affect the property price.

Nonetheless, the idea was quite appealing and made a lot of sense. And I started wondering why it has not happened already. Possible explanations might be that whichever city implements such a policy, the perception is that this city will become less competitive for corporations and potential investors who can always move capital to cities with lower taxes. The challenge would then be introduce an element of reward for early-adopting cities that can offset the initial misgivings about making the city less business-friendly that can serve as exemplars for other cities who will then adopt such a policy to provide free public transport paid for from property taxes. Can someone suggest a way to solve this problem?