I think you are conflating active and reactive loads. Reactive load is basically EM, not heat.

Yes, reactive current is still current and any series active load (wiring) will experience that current and heat up. The reactive load itself is "imaginary".

I'm aware it's EM but I'm pointing out it's dissipated as heat through wire current. I'm aware it's imaginary, doesn't mean it doesn't produce electrical load in the wire.

Besides, for any reasonable heater arrangement, this loss will be negligible compared to any other heating mechanism.