That's a disaster waiting to happen. Those caternary wires are deadly. And you want Joe Blow from down the street to be connecting and disconnecting his car to them on a daily basis? One mistake raising or lowering the pantograph, and Joe is getting lit up like a Christmas tree.
As soon as highway speeds hit 30+kph became possible the death rate from petrol fueled cars became a disaster. In the 1960s the automobile accident death rate was pushing above 40,000 per year in the US. Some folks wrung their hands over it but most took another swig of beer and hit the accelerator. Electric trolley accidents were not uncommon in those days.
What about if we don't need cars for majority of travel ? Could really cheap and widespread railway network develop ? and possibly subway / tram in cities ? an European / East Coast wide version of Japanese Shinkansen with subway in cities.
That can work in densely populated areas. In the US its better for most folks to use the subway/train in a few cites. Even with heavy subsidies its tough in the other 99.99% of the US to come close.
1st Problem is taking the overhead DC voltage(600V at minimum), and getting that to a voltage and current level that won't smoke your battery tray. For WWI era, easiest way is a motor-generator set.
2nd is rubber tires prevent a ground path to complete the circuit to Ground/Earth
So you would have to drag a long steel chain(s), like a drag harrow, to hope to make good contact with the street rails for the circuit to complete
A closer look at the technology is necessary here. I suspect there are some good workarounds from the technical PoV, but those may not be cost effective.
Yet another direction is swapping out battery trays at the road side service station. Again that may or may not be cost effective, but can be technically feasible.