IGBT ZVS Induction Heater?

Among the many tutorials for building an induction heater out on the internet, there are two primary types. Some heaters use a ZVS circuit, and are quite simple but generally limited to a power of around 1000 watts, not enough to melt most metals. Other heaters use PLL controllers and coupling transformers to add charge the primary coil/capacitor loop, and these can be much more powerful but are significantly more complicated (and expensive) to build. It seems the limiting factor in the power of the ZVS circuits is that they can use only 2 MOSFETs, and each must conduct large amounts of current. However, if these could be replaced with IGBTs, which could conduct far more current, a much more powerful ZVS induction heater could be built. Is there any reason IGBTs couldn't be used for a ZVS heating circuit?