Inductive charging has two major drawbacks: efficiency and RF noise. If the loop is as big as the space below the car allows and the positioning is very precise and the distance between the loop and the car's receiver is very-very small, we're still looking at 5-7% energy loss. There's (almost) no way around it. These 5-7% (realistically, though, about 10%) go into heat AND RF. A ~1KW RF signal is a powerful source of problems: it will inductive heat lots of things around (and below, like rebars) the charger. Also, FCC might want to have a word here as well.
Most of these problems have known solutions, but they are costly (moving parts, multiple coils with precise positioning, active shielding, etc.) and once you start mitigating them you're quickly surpassing the cost of a well-designed contactor.
Under car connector -- a doable solution. Removable covers against dirt, moisture and frost and precise positioning (probably active homing from the ground side) are much easier problems to solve, IMHO.