i use seasoned cast iron for most all my stove top cooking that require searing or use like steak, eggs, sauteeing or a steady consistent heat maintained.... a well seasoned castiron pan the food wont stick they are easy to clean and care for overal but to take a little more care they a cheap throw away pan like most use and yes on occasion some pans may and will require seasoning again at some point during its lifetime. I still have and use the cast iron cook ware my grandmother and aunts had and it will still last for generations to come if properly maintained
The stoneware type pans kettles or roaster pans dont have the heavy gauge thickness to pull and hold the heat like a cast iron pan and sadly extreme point heating can cause fine cracks in the stoneware enamel coating. and then the other type stoneware that is made from granite also reacts differntly then will a castiron on its heat retention
the non stick yoyu use for your egg is propably heavy enough to hold a good heat, this is one key to cooking that most never learned or was never explained searing /browning /caramelizing the outside to hold in moistures is a primary purpose of pan frying of many foods and easier to maintain a consistent heat like a fried egg or omelet to hold stead medium heat across whole surface.
option if you dont have a castiron pan . heavier type steel pan they can season and holdheat like castiron ( woks at a heavy carbon steel hammer and shaped ), a heavy type dutch oven is very versatile it can be used stove top or in oven to braise sear and cook on stove top, you can roast poultry and meats even bake breads in it in oven and its usally is heavy enough to hold and buffer the heat better the a thin metal , ss, or aluminum fry pan