I think that perhaps this should be in brainstorming.
However there are some points to note:
London is partially implementing this idea, by having a fare differential - if you have an Oyster card, then your fares have been frozen, if you don't then prices are rising rapidly.
http://www.bbc.co.uk/london/content/articles/2005/10/04/bus_tube_fares_feature.shtml
So what is the Oyster Card? Well obviously it is a "Smart Card" (RFID tag) that takes the money off you as you complete journeys (within a limited area - see the complaints in the above link). To get one you need absolute proof of identity, because that is already a demand just to get the basic Photo ID, which is already compulsory in order to get a simple Weekly Travel card. Visitors to London area already hammered for using public transport, because unless they carry their passport, a few utility bills and have two additional passport photos etc, they cannot get the photo-card.
http://www.tfl.gov.uk/tfl/fares-tickets/oyster/general.asp
So having been proved a "success", it is most likely that the Oyster Card concept will be rolled out rather than coming up with a new idea. However, as the terms "Smart Card" and "proof of identity" imply, and following the detail of how Oyster charging works, you discover that TfL are tracking every journey that the Oyster Card User makes. Big Brother IS watching you if you want to save money. With Oyster working so well, why would they slip back to a simple Photo card?
The possibility of free public transport actually happening is zero. Absolute zero in fact - so damn cold that nothing at all moves. There might be a price differential (as with Oyster). but free? No.
Now it might surprise you, but even when I lived on the outskirts of London (25 years ago),
nobody chose to drive from Putney (or in my case Kingston) into the City unless they absolutely had too. And I did once because I was playing in a band, and we had a gig in the Rock Garden in Covent Garden - for some reason the idea of trying to take £3000 of kit consisting of 2 hard-cased guitars, amp/effects rack, 2 speaker cabs, mikes, mike stands and guitar stands on public transport wasn't exactly practical - never mind the possibility of theft (which was a strong possibility), the bulk and weight made it impossible. But even then it wasn't easy with non-existant parking, and unloading involved a 100yrd carry.
But I do know people that do drive into London - a relative of mine is involved at senior management/director level in a number of companies based in central London, and he lives in a very nice house out in the country, and he drives in every day. Parking isn't a problem because the offices include very limited parking spaces which he could obviously use, and almost no level of charging would prevent him driving. Free travel would make absolutely no difference to him, although he does use the train if he plans on having a few drinks.
What I am trying to say is that for London the price differential between public transport and road use is already heavily biased towards public transport, and that for anybody that has the option, Public transport is already the mode of travel of choice, and the rest are simply not influenced by price - even if you paid them to use Public Transport they wouldn't.
Not that public transport actually has the necessary capacity to carry the people at times of peak demand - which is why prices are actually increasing, not going down with higher usage.
For those further out without the decent public transport - i.e. anybody not actually living in London or a few select city centres, then they have no choice at all. Many people live in areas with zero buses, or nominal once a day services which for some reason never coincide with possible demand.
Would free fares (and detailed tracking of my movements) make me use public transport?
No. For the simple reason that even in my moderately well covered area it still isn't practical. Public transport is fine if you are carrying nothing, or at most just the quantity that a person can comfortanbly carry. If I need something small, then I walk to the nearest shop, otherwise we economise on the journey by buying as much as we can in a single trip, and typically stuff the boot full. I cannot replace that trip with public transport.
Could I use public transport for leisure?
Again No. It doesn't matter how much it costs - I now play golf, and never mind the fact that public transport doesn't go to the Golf course, but the equipment is again too bulky and heavy.
Would I use it for holidays?
Absolutely not! Are you crazy? We have a toddler that still sleeps in a cot. Even a simple 2 night stay with the grandparents involves taking: folding travel cot & mattress, food, drink, toys, clothes, changing mat, nappies, pushchair, and a few bits for us. It is a stuffed boot full, and given that one person would have to be holding the child, this leaves a single person struggling with twice their volume of stuff to move.
In conclusion, what you are suggesting is that the rural people, others with minimal public transport links, families and anybody else that needs to move more than a simple bag of stuff with them, should pay a lot of money to subsidise those without any such restrictions. It isn't price that stops most people using public transport, it is the practicality.