It's little to do with voltage or current, but power which is the combination of both. You maybe able to get 0.2V from an inductive loop near to a transmitter, but the current available will be very low. The Thevenin equivalent resistance will normally be too high to make use of the the current available. Likewise a high current induced will have very little usable EMF. Adding a convertor as shown above just moves the problem from high voltage low current or low current high voltage. It doesn't help either way. This is not even taking into account the conversion factor.
You cannot get something for nothing. One of the laws of thermodynamics and I cannot remember which one. Energy cannot be created or destroyed.
If you are lucky (or unlucky in my eyes) to live so close to an AM transmitter putting thousands of watts into the ether, then with a farmyard of coils, you maybe able to light a 1mw LED at 1000m. Hardly worth a gong.