Cast iron and carbon steel have their care quirks but also have performance characteristics not available in other cookware. All have their time and place.
Cast iron can be heated to brutal temps that will destroy non-stick pans, warp aluminum or clad pans. So you can lay on a fabulous sear for a steak, blacken fish and so on. And it is still very much non-stick. On the other hand, cast iron is a pretty poor conductor of heat, which is part of why it retains heat so well. If you use it on an induction burner, you can heat the part over the induction coils to very high heat while the rest of the pan remains much cooler. Induction is very fast at transferring heat to the pan and really shows how slow cast iron conducts.
Carbon steel, like cast iron, can take high heat and be quite non stick. It will warp however. It is also a better conductor of heat. These traits are good for the wok for example. Non-stick surfaces can't take the heat of wok, nor the stirring action with the specially shaped spatula. Carbon steel is less reactive than cast iron but doesn't hold the seasoning as well as cast iron either.
Both cast iron and carbon steel pans lay on a sear and generate fond like a stainless clad pan while still releasing like a non-stick pan. Nonstick pans are very poor at browning.
Remember, the original claim to fame of a non-stick pan was easy clean up, not it's great cooking properties. I like non-stick pans for eggs, fish, and many one-pan casseroles. I love my cast iron for cooking potatoes, meat, pan cakes, dutch babies. If I'm just frying eggs, I'm happy to use cast iron. It's more when it comes to scrambles and omelets that I reach for non-stick. I have one 10" cast iron pan I can do omelets in, but its still a bit finicky compared to non-stick. I have cast iron muffin pans that I pre-heat and make a great popover in. The heat stored in the muffin pan really improves them . I have two cast iron pizza pans I've come to prefer over a baking stone for breads and pizzas. They also double as a great griddle.
Coated cast-iron is nice to cook in too, especially for soups and stews. I find it more finicky about care and harder to clean than cast iron, but admit that comes down to personal preference.