I find cast iron to be a bit heavy for everyday use, carbon steel gets you most of the benefits while giving you more flexibility on the weight.
The only thing I use my non stick for is omelette dishes mostly because it’s much easier to fold French omelet when you can lift the pan easily with 1 hand.
You can certainly cook eggs in a well-seasoned cast iron. I just like to do french omelets which requires you to stir things before it sets, which is a bit more difficult on seasoned cast iron or carbon steel vs just a plane non-stick.
Both of my carbon steel and cast irons are larger 12 inch pans, so they are both a decent weight.