Maybe my world view is limited, but I have never seen an application of the rail system on a small scale.
For instance, I have been to parks where they have small train rides for guests. However, I have never come across a real world application of this for transportation purpose.
What I envision is not a train, but a means of transportation that utilizes the rail system. Imagine an item with the shape and width of a skateboard or hoverboard. Now, imagine a narrow rail that this object can fit on snugly. This object will have internal gears that will interract with the rail and propel it forward. And to ensure people can keep their balance and not fall off while it moves, there will, quite naturally, be railings by the side they can hold on to.
For sustainability purposes, the entire system will run on electricity.
There will be an operator for this apparatus who will control the running and ensure people pay for using the service. It can operate like a train or bus station: commuters can only use it at certain, pre-set periods.
Also, this invention is not a train. As such, it should operate within short distances only. People can hop from one terminal to another if they are going to longer distances, much like we already do with trains.
This idea also uses the rail system. However, instead of having a skateboard-like device, there will be a scooter-like device with a pedal attached. The user can then use this pedal to propel the apparatus, much like a cyclist does.
Replace the scooter-like device with a seat and the idea still works.
This occludes the need for electricity, and makes the devices easier to operate.
What is the Merit of this Idea?
Such an application of the rail system will, obviously, cost less than the train or electric rail car apparatus. Also, it will be easier to set up and maintain, thus making it an ideal fit for developing countries.
By the way, it will be a slow means of transportation. But that is the price to pay for its low-budget nature.