Bram

Thin and light is the trap when buying cheap. Thermal mass is most of what a skillet is for.

Took a flap disc to a rough modern pan and it worked, with two warnings nobody gave me.

It takes longer than you think, closer to an hour than ten minutes, and it removes the seasoning entirely so you are starting from bare iron. Budget an afternoon for the sanding and the first three seasoning rounds together, or you will end up cooking on bare metal for a week.