Yeah. I get that. I think it is an excellent design.
By adding a third rail in acceleration and deceleration areas you would greatly increase electrical efficiency and reduce battery requirements. You wouldn’t waste power charging and discharging the batteries during deceleration and acceleration. Additionally, the battery would only need to be able to provide enough power to maintain the speed. This also reduces the weight of the vehicle.
A 3rd rail massively increases the complexity of the setup. The tracks are shallow and simple. This makes them cheap to install. Adding a 3rd rail hugely increases the complexity, as well as adding safety concerns. It would be cheaper and safer to add additional chargers, mid route.
How does it increase complexity? It seems like it would be simpler than this mechanised charging system. A third rail wouldn’t prevent the tracks from being shallow and simple.
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.