I've never heard of pedal-powered vehicles being banned from roads anywhere in the world, including in countries that do have a lot of bike paths but excluding controlled-access roads where speed limits* are in excess of what utility cyclists (in everyday clothes on road-going bikes) can achieve.Apparently they feared that if there were proper cycle paths cyclists would be forced onto them and banned from using any normal road even if there was no cycle path alternative. To be fair there are plenty of drivers who want bikes banned from the roads and are also bitterly opposed to any cycle paths being built anywhere.
But bicycle storage on trains does exist, and this depends on the trains. If you make the trains larger, then at least upright bikes can be carried, often stored vertically, possibly even at busier times.You can't really take many bikes on a crowded commuter train during rush hour.
*This sometimes applies even to minimum speed limits.