How you'd do pan sauces with anything but a stainless steel pan is beyond me. You can do it, but if you took care of your cast iron skillet the way people suggest, you can't get any fond to create the pan sauce.
And you cannot cook good eggs on anything but a non-stick pan if you're not working on a commercial, well-oiled skillet, which is a different beast all together. Shakshouka doesn't count.
No clue what people are talking about when they say you shouldn't clean your cast iron either, it's disgusting to me. It makes no chemical sense. Sure, you've got the pan seasoned, but as soon as you cook anything in it, it will transfer, and there's no amount of wiping that will prevent that. None. If you salt it, you will transfer salt.
Cook with it, clean it thoroughly with soap like you would anything else, dry it immediately, and then just use it again. Any amount of neutral oil you use to cook with it in the future is going to effectively do the same job as seasoning it. Occasionally seasoning it should be fine if you have to restore it for some reason, but you'll end up washing it again anyway.
I agree with the notion that it's strange to treat cast iron with such esteem when it's far easier to screw up stainless steel and have to restore that, which is far more labor intensive.