I've got a stainless skillet. Every single time I fry eggs like that, without > 1T of fat per egg, it burns to the bottom. So you must have a better technique. I'm willing to switch to a more forgiving option rather than keep scraping off my mistakes. Every time.
Also, don't be afraid to use however much fat you need, it's not like you're actually going to eat it all - there's probably only going to be about 1/2 teaspoon of it left on the egg after cooking regardless of how much you put in the pan and that's (probably?) pretty negligible health-wise.
The key is adding fat just moments before adding the food, and adding just the right amount of fat (which is more than people realize).
I cook eggs on high temperature in butter and steaks on high temperature in olive oil, and I never burn my fat. You can only do this for one portion though, if I use the same pan to prepare multiple batches, I switch to lard instead of butter/olive oil. I still like to finish my steaks in butter though, but I just do that as an extra step at the end.
As an unrelated note, I very much prefer lard or duck fat, or if they are unavailable then coconut oil or some other kind of saturated (?) fat, to vegetable oil. Not because of taste (lard is good though), but because the surface tension is different for these solid (at room temperature) fats and these fats coat the pan much better than any kind of vegetable oil. They coat the pan instead of pooling up.
In fact, butter and olive oil are more difficult to use, and more prone to scorching with non-stick pans because of lower thermal mass, which makes it much harder to regulate temperature.
The temperature of the pan needs to be the same, regardless whether it's non-stick or not, in order to produce good results. If you start with a cold non-stick pan, the food won't stick, but it will be of far less quality than if you had started with the proper temperature.
So I guess that non-stick pans allow you to more easily make bad food without making a mess, but that's not a metric that I care about. If you care about the quality of food, non-stick pans are more difficult to use because temperature control is harder, they can't get as hot, and generally you can't put them in the oven.