"I had a go at rewinding a wire-wound log pot one time, it survived a
year and then something went wrong. "

I repaired a variac a while back. Obviously it was linear. Luckily I caught it in time as it was rubbing the wiper over a winding that was popped out of place and it would have broken soon.

But don't confuse a variac with a pot, a variac actually works like a transformer. Now if one were to feed it DC it would be nothing but a pot, and likely burn up unless you kept the input voltage down.

But a little bit of glue took care of it, good thing too as it was one of the ones that go up to 150 VAC.