[kwhitefoot]

> whatever current is induced there, you have to put it somewhere.

No you don't. What is induced is an electromotive force, e.m.f., that is voltage. If the coil is open circuit then no current will flow. It's slightly more complicated than that because wireless charging uses tuned circuits not simple iron cored transformer but the general principal is the same and the control circuit in the phone can simply disconnect the coil completely in order to not accept any power.