At the level of mass commute cycling in busy urban centres it doesn't make sense to take a bike on the train, terrible use of space if tens of thousands of folk try and do it. Hence the model of cycling to the station, hiring at the other end.

One approach, originally from Japan, I think, is to "Rinko" your bike. With a few optimizations, you can break down a regular bike in short order and stuff it into a bag for train travel. www.rossmancycles.com/rinko

Yes, that's really a problem. On regional trains you can take your bike. Sometimes they are to packed. So it may be better to check out before you go.