What if we have renting spots for electric bicycles beside the train station? I think that would be a great idea.
Imagine that, you just get off the train, and you are so tired that you want to reach your home as soon as possible. Renting an electric bicycle would be a nice idea. Taking the bus may also be another option, but you have to wait for a certain period (maybe the bus is just cancelled because the buses go on strike). When the weather is freezing cold, waiting for the bus will be a horrible experience. Anyway, I have many bad memories of waiting for the bus… Another reason is, there are many uphill and downhill in Leuven (and also other cities in Belgium), and owning/renting an electric bicycle can do you a favor to ride more easily.
The drawback or the problem we still need to solve is that we have to build infrastructures, such as the parking spots and charge stations. And you have to keep an eye on the electric bicycle you rent, there is a risk that it will be stolen…
Here is an example for renting an electric bicycle in Tokyo: http://tokyocheapo.com/travel/rent-an-electric-bike-cheap-things-to-do-in-tokyo/
What’s your opinion then?
e-bike powertrain efficiency 
Very good idea but like you said you need a big infrastructure for that. Charging stations enough safe places to put your bike etc.
For big cities I can see this work but not for Leuven.
Very good idea indeed, but like Bram V says, I also think that it would be to complicated to actually carry out. In fact, such a system would have to be really simple and user-friendly, because otherwise people would just still use their own bike (or even worse, their own car). I do however think that the electric bicycle should be more promoted as a really good alternative for cars.
I see a lot of potential in such a solution. In large cities, like Brussels, there are already such systems in place, but not with electrical bikes. In the Netherlands you can pick up a bike at almost any train station for 3 euros per day. Extending this plan to electrical bikes seems like a logical evolution.
What you said bas already applied in some train station such as Antewerp Central station but they are not e-bike they are just regular bikes. But it does seems to be too popular the amount of bikes are also limited. This could be better if we applied such a infrastructure in sight-seeing spots, especially with large area.