Also importantly, the more complex the cable is, the more expensive it will be to replace if someone comes along with some bolt sheers and clips the cable.
Our "current" (pun intended) cables can deliver 350kW of juice. That's already more than most car battery chemistries can accept for more than a few minutes before doing harm to the battery.
Not to mention the fact that even if you could deliver such high amounts of power, that'd translate into insane requirements on the grid, likely necessitating onsite storage to act as a buffer.
All in all, the recharge time problem is overblown. There isn't as much need for high speed charge infrastructure as you'd imagine. That's because most charging is happening at home at lower speeds. Your car almost certainly sits idle for more than 8 hours every day which is plenty of time to refill. Fast charging really only matters for long range excursions, which aren't terribly common.