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.