Fried eggs on Teflon pans are rather soggy in my opinion…
My preferred pan for fried eggs is stainless steel. With plenty of butter the eggs crisp up and release from the pan with no stick at all. The only real trick is to not flip too soon.
The scrambled eggs my girlfriend cooks on the $10 stainless steel, well greased pan blow any eggs I have ever made on any "nonstick" or "seasoned" surface so out of the water that I no longer consider nonstick pans to be anything more than a mild convenience. I have one nice one that I use for general cookery and only rinse out, and it has stayed super non-stick.
I legit went through 2 dozen eggs trying to get a perfect fried egg on stainless steel. I tried everything - hot pan, cold pan, oil, butter, swirling the pan, a touch of vinegar. I could not find any combination that worked - I suspect that you either have to have very particular equipment.
You can cheat with a lid - just seconds the whites would be in your preffered condition (ie with/out crust) cover the pan, sing aloud 'We all live in the yellow submarine, yellow subma' and move the pan off the stove, but don't let it rest under the lid too long! In 20-30 seconds it would catch to be the nice, yet runny one, but anything longer and it would be more thicker, though if you like subs/burgers with eggs - it's a way to it.
PS you can sing something more palatable for you, if you wish *grin*
The trick is to let the pan get to the right temperature. You don’t want it super hot, but you need it hot enough for the Leidenfrost effect. You can tell the pan is hot enough by splashing water on it. The water should not boil, but rather bead up and roll around. It takes a few minutes of heat to get the pan to this temperature. Once you reach this temp, the pan is basically nonstick as water in your food instantly vaporizes and creates a barrier between the food and your pan.
Most range levels can get to this point, even medium-low, but you need to leave the pan on the heat for some time before starting to cook.
Try more heat. It needs to crisp at the bottom while staying runny at the top. Don't let them sit in there once done, get them out to stop the heat transfer. I only do one side.
Over easy is easy on cast iron. I tend to put a spoon of butter, spread it a little, and crack the egg into it. The butter should sizzle but not brown too quickly. You should be able to slide the egg in the pan like on a nonstick.
My preferred pan for fried eggs is stainless steel. With plenty of butter the eggs crisp up and release from the pan with no stick at all. The only real trick is to not flip too soon.