(1) not all transport is public (2) you'd have to make up for income losses for public transport companies with increased taxes, but now instead of driving income for public transport companies through market demand you're creating subsidies, which creates an organisational culture that's not consumer-oriented but rather oriented towards the government that subsidises it.
Anyway there are pros and cons, these are just the cons. If you ask me public transport would be a big source of investments and a completely free service like say the justice system, public roads, parks etc. Moving about the city in the safest, most efficient, cheapest, cleanest and environmentally friendly manner that's mass transit (i.e. ignoring say bicycles) should be free if you ask me.
How would you allocate the money between mass transit (RATP), long-range transit (SNCF), bike rentals (Vélib) and electric car rentals (Autolib) ? And this is for Paris alone.
Now that smartphones are becoming ubiquitous, I suspect it could even be done statistically. Create a good transit app with embedded tracking. You'd know where people were trying to go to, how they ended up getting there, how long it took, etc.
Do that and you could eliminate all of the overhead of ticketing, charging, etc. It wouldn't be perfectly accurate, but it's not like the current system is either. [1]
A group which, on present evidence, is about 0.1% of the population, which would not be a big problem for the scheme. But there's no reason to make it mandatory in that the goal is to make transit free and allocate money statistically. No harm would be done by putting some obscure checkboxes deep in the settings.
