I've dedicated myself to figuring this out. It's not that you have to drench it in oil, but there needs to be enough to cover the pan.

The most important part though is that the pan is heated up enough when you crack eggs on it. And give the eggs a little bit of time to cook before flipping them.

It takes a lot of practice and you're going to be eating scrambled eggs instead of fried eggs for a while. But keep at it.

Have a ceramic pan dedicated for sticky stuff that doesn't need to be cooked too hot. Ceramic that is not used on high heat lasts a long time. Obviously with wood of silicone utensils.

Eggs are indeed tricky on the stainless. I have found that ceramic or a well-seasoned cast iron pan is a lot better for eggs if you aren't good at hitting that exact temperature that they need to be at to cook and release on their own with just a minimal amount of oil/butter. My parents have a single teflon pan that is just for eggs, but they cook eggs so frequently that they need to replace it all the time because it starts to peel and flake in no time flat.

You might be cooking to hot, I use cast iron so I can’t speak directly about steel but low and slow is best for eggs on cast iron.

Well-seasoned, smooth bottomed cast iron or carbon steel can be great egg pans. There's a learning curve but IMO the maintenance isn't as daunting as many think.

I've got a de Buyer carbon steel pan that we use for eggs most mornings; it doesn't perform identically to a Teflon pan but it's still very very good. Maintenance is just (1) a drop of oil before the food goes in, (2) quick wipe under the faucet with a dish brush, and (3) dry with a dish cloth before putting away. I've had the pan for almost 10 years now and there's no reason it shouldn't last the rest of my life (and then some).

Just use cast iron at that point. Season it well enough and it'll be smoother than any nonstick you can buy

Unless you drench the pan in oil.

Nah, you can develop technique to prevent this. What's great is on stainless you can use a stainless turner as well. When it comes to eggs it's all about adding enough butter to cover the bottom of the pan and then keeping the egg moving after the initial side is cooked enough to release.

Omelettes are the same on stainless. You just have to keep things moving. It requires a little more technique and attention but IMO that's better than having a side of Teflon flakes with breakfast.