Are you sure about that?
Just looking on the Wahoo website and it says that the Kickr Power adaptor is 12v DC output at 5 amps then it says Max 60 Watts.
Maybe I don’t understand how they work, but I thought they were an electromagnetic brake. If I’m riding at a steady 200w for an hour surely 200w must be provided to the brake to provide the resistance?
Edit: quick look suggests they describe them as using a motor, so I guess they add resistance to the motor that produces heat. That makes sense, so I guess you’ve got it right. A battery setup should work.
As an aside, if something has a 12v DC adapter you don’t need an inverter to go up to 240v, just go straight to the battery (without the adapter).