For the geek part: when trains shift from one network to the other (RER B between Châtelet and Gare du Nord), they free-wheel while they transition power from one network to the power of the other one. On the rare occasion that a train has to stop in the middle of that dead zone, it can't move anymore...
The US half tries to fund and administer infrastructure at the federal level, state level, as well as local level, depending on the state.
As an American, I find the EU to have phenomenally good infrastructure, but I think that's because decisions aren't being made in Brussels, they're being made concurrently in Paris, Berlin, Amsterdam, London, etc.
I feel that the US would do well to emulate the EU, and centralize the funding, regulation, and administration of its respective systems in each member state.