This seems like such a no brainer to me that I wonder why it wasn't implemented much sooner. The biggest problem seems to be how to handle increased demand. But increasing demand is exactly the goal of this measure!
It's going to be expensive. With EU fines of a couple hundred million euro looming for missing air pollution targets and not doing enough to work towards them, spending that money is getting more attractive. + giving people stuff for free is a lot more popular than other options, e.g. temporary bans of diesel cars etc. (both with owners and the poor, poor car companies...)
I don't think that this is such a good idea, as mentioned above by others, during peak hours the trains are almost over capacity (At least in Munich where I currently live). Making them free would lead to a degraded experience for everyone.
One of the major reasons that I am not in favor is because in Pakistan ( where I am originally from) they launched a Metro Bus service a few years ago, the fare was a nominal flat rate ( ~ 15 euro-cents) for traveling as much as you can in one direction. Now although it is a great service for the people but the buses are always over crowded, and because they are incurring a loss and the government has to spend millions of dollars per year in subsidies just to keep it afloat; They have not upgraded capacity and it is really inconvenient to travel on those buses ( I remember getting sick 4-5 times a year when I regularly traveled on those buses).
A better solution would to be start banning the diesel engine, ramp up the taxes for fossil fuel based cars. And to force factories to reduce their carbon emissions.
