Use a wooden frame to avoid dissipation of high-frequency current?
He seems to be suggesting that if the machine had a metal enclosure, it could somehow leach power out of the circuit ...


Of course! That's the whole idea of how induction heating works: A strong magnetic field is used to induce a current in a conductive material, and that current is converted to heat by the resistance of the material.

The magnetic field can't discriminate between "target" and "enclosure" &mdash; ANY metal (or other conductor) that it encounters will be heated. And if any part of the enclosure forms a complete path (a.k.a. "shorted turn") around the coil, it will absorb MOST of the power being applied and heat up very rapidly.