If you do this correctly, even eggs can be prevented from sticking on stainless steel pans. The extra advantage for stainless steel is it can be cleaned back to like-new condition relatively easily and without significant concerns over /how/ you clean it. You can even use acids to clean stainless steel to polish it to a shine like vinegar or lemon juice, without damaging the metal in any significant way.
The advice to pre-heat the pan first is because if you forget an empty pan on the stove you get a hot pan, if you forget an oiled pan on the stove you get a grease fire.
Also try out carbon steal for a more nonstick type situation. Stainless is best when you want some sticking, like for building a fond for a pan sauce. Carbon naturally seasons similarly to cast iron, but much lower maintenance because you can wash it however you want and essentially rebuild the seasoning from scratch for each use.
1. It matters because oils oxidize rapidly (and can begin breaking down) in the presence of high heat. You want the oil to be relatively fresh while using it to cook. This is less of an issue with highly refined oils, but a problem with most natural oils.
2. Oil isn’t affected by leidenfrost, but the food you are cooking is. This effect prevents the food from falling below the oil layer and sticking/burning to the pan when the oil is moving due to water boiling off. When water molecules in the food come in contact with the surface of the pan below the oil, leidenfrost forces them to float back above with the food and allow oil to flow back into the space.
Moving food as you cook it helps with this as well. If you cook at the wrong temperature without this effect, oil gets displaced from below the food and it sticks. This is especially difficult with very wet foods with minimal structure like eggs.
No cooking oil is going to appreciably oxidize in the 70 seconds it takes to heat a pan. I cooked at very high levels for many years, I have seen a cook get fired on the spot for handling a pan incorrectly, no one cares about whatever oxidation is happening during preheating. The advice to add oil to the hot pan is so you don't forget and overheat the oil, or start a fire.
Side note, many people cook with way too much heat.
However, I've never gotten scrambled eggs to work without just coating the entire pan in egg.
Scrambled eggs don't play nice with high heat, and too high heat and the butter will brown or just burn. I can absolutely coat the pan with butter, and the eggs still stick.
Not sure what the solution is here.
Stainless steel, while typically being derided by many home cooks for being "hard to clean", is actually quite pleasant to work with if used properly. What does that mean? Well, I've discovered that it means you should start with high quality pan (I use All-Clad BD5 and Copper Core, though there are many other good options too), heat it up fully before adding anything to it, throw in some fat and wait a few seconds for it to heat sufficiently, then add your food. Keep the heat up while cooking (good pans help with this part a lot).
Try it and thank me later. It changed my life. :)