I've got two Indian
karhais, like perfectly round-bottomed woks, that I think are carbon steel, and wow, they're great! I've managed to browbeat and train and nag my housemates until now they know how to treat them right, so the pots are gloriously non-stick, beautifully tempered. It helps a lot that the round-bottomed shape is perfect for making popcorn, and popping corn in oil is the quick and easy way to refresh the surface.
Cleaning -- I don't mind a quick swirl under
water with a steel scrubby, and even some
soap, sometimes. Once it's got a good surface on it, those won't damage it. And of course put it on the gas flame to dry for a few seconds to prevent rust. If it's only greasy, because you just slid perfect fried eggs intact out of it, then you just admire it and leave it on the stove till the next meal, or maybe wipe off a loose bit with some paper.
I don't know if Indian groceries in the US
sell these -- they might only stock non-stick or aluminum karhais, but if there's one in your region, it's worth a check. An Indian carbon steel
karhai would be a fraction of the cost of some of the pans mentioned above, and I find the round-bottom shape really great -- by far the best for fried eggs, and popcorn, and also excellent for normal cooking where you start by heating spices in oil, then add all the other bulky ingredients.