Trains are not all the answer in my opinion. They can be part of an answer but not the whole thing, not here in this country. If you had to have a train, then the only sort that would meet the requirements of a daily U.S. commuter is one that is made up of self-contained pods (let's call them cars) which can join up on major arteries at high speeds and then break off autonomously for self-drive mode on suburban roads when the proper point is reached. Add in self parking and retrieval via smartphone and it's the same idea.
It's not that wholly different from what Lutz described and simply takes up a bigger space footprint. Space is something we have lots of and it's both a benefit and part of the problem.