If you could somehow make the cores contact by either lowering the car or raising the primary winding from the floor, then the system can be made a lot more efficient, but at that point:
1. You're introducing robotics and moving parts into the floor unit, which is what you were trying to avoid. Or you force all cars to have air suspension, and many don't.
2. You now have an alignment issue, because the core will heat up with hysteresis and eddy current losses if the two parts aren't aligned.
3. If you're making something in the floor contact something on the underside of the car, then at that point you could just do electrical contacts and eliminate the transformer entirely.
No matter what, the secondary of the transformer in the car adds weight and impacts efficiency.
Further, the transformer can only transfer AC, thus your power limit for charging is the limit of the on-board chargers -- 20 kW max or 10 kW in the majority of cars which can only reduce the full-charge time to 4.5 or 9 hours. For anything faster, you still have to have the charge port so you can charge with DC.
Seems more trouble that its worth, given that a robotic arm is straightforward, compatible with all cars, and has no efficiency losses compared to standard charge cables.