Maybe we can do away with the expensive battery if we feed power to these cars using overhead cables.

At this point overhead cables are likely many orders more expensive.

Buses in Paris run with IIRC 60kWh battery and pantograph charger at every other station. Packs (not cells) recently dropped to below $100 kWh. At $6k thats probably what city pays for couple of replacement seats (gold plating et all).