A 3rd rail needs to be designed to play nicely with what’s around it, e.g. kids poking it with a metal pole. It also requires power to be delivered to it. It also requires a way to repower a section when roadworkers need to move the rails. It also turns a run of paving slabs into a full blown circuit, requiring more training to install.
If you’re intending it to only be at the stations, then you still need to deal with the curious kid issues, as well as dealing with weather related issues. E.g. what happens if the 3rd rail is in a 5cm deep puddle?
The other option would be inductive charging, from below. That has its own problems however, the biggest being efficiency.
I would only power it when there is a car on top of it. That was done a hundred years ago. Now it is much easier. It just takes an IGBT per section. Seems pretty easy.
Magnetic Resonate wireless chargers are about 90% efficient but it seems that is a lot more complicated and expensive. Still this seems like an huge improvement over those charging stations.
I don’t see any reason to charge from the top of the vehicle no matter what method you use.
Charging from the top means you can easily keep the public away from the contacts. It’s also easier to keep things clean. It might also be a factor that you don’t have to dig up the road to add a new station/charger.
There was likely some cost/benefit analysis done that found it was cheaper/more reliable/less logistically complex.
