If there is anything I hate more than crispy, hard and stinky fried eggs, I'll be sure to tell you about when I remember what it is. Eggs that are fried too quickly in a pan that is too hot coagulate too fast and dry out. The result is hard whites and yolks and crispy brown or -god forbid- blackened bottoms. Moreover, such eggs end up stinking of hydrogen sulfide because, of course, they got too hot.
I prefer fried eggs that are tender, runny and with little to no browning on any surface. Now while the reason I prefer to cook eggs this way really boils down to a matter of personal preference (i.e., "That's the way I like them because that's the way I like them."), it's a preference that turns on a philosophical point. I'm of the opinion that if I am lucky enough to have food that is very fresh and of very high quality, the best thing I can do to it is the least I can do to it. My goal is to maintain the character of the raw product as much as possible and not transform it into something that bears scant resemblance to what it was before I cooked it.
Eggs are pretty subtle zygotes: no matter how good they are, their intrinsic flavor and texture is very easy to bury under careless technique. They are arguably best eaten raw, at close to body temperature. So if agree with me, then when you propose to cook an egg you would do well to ask yourself how you can preserve as much of the character of the raw egg as possible yet still regard them as cooked.
Now while the specifics of the answer you get will depend on what process you plan to put the eggs through (e.g. poaching, scrambling etc.), the basic technical challenge will always be the same because how an egg changes as it heats is ultimately determined by its physical composition -which varies very little from one egg to another. Sure, some eggs will be fresher than others (lower pH & more water) and of course, you can alter the physical properties of the egg by mixing in salt, or some other substance that affects the behavior of the proteins or alters the ratio of water to protein (as would be the case if you added wine or milk). But even then, if do not heat the eggs gently they will still become tough and squeeze out water. Here's why in a nutshell.
Egg whites and yolks are suspensions of protein in a watery and fatty (in the case of yolks) medium. When they heat slowly, the proteins open slowly, collide gently with the other proteins and form a loose spongy gel structure that traps the water. Heat the eggs too fast though, and the proteins open quickly, collide too often, bond too many times and create gel structure that is so tight that the water gets squeezed out resulting in a hard, dry cooked egg.
Of course there is a lot more to the story than this. For example, if you get the egg too hot, the water in the egg also gets too hot and evaporates too quickly. Also the proteins may "blacken " and begin to break down and release stinky amino acid compounds (similar to what happens in overcooked fish)...I could go on but I'm out of time.
Okay about this video.
I did it in one take because I only had two eggs. So it's a bit rough. My narration is unrehearsed and punctuated by really annoying coughing - the natural consequence of asthma and allergies. I'd love to be able to edit that stuff out but my software is not up to it. I also misspeak slightly when I say the pan needs to be pre-heated to 350 degrees F. That number only works for the kind of pan I'm using and the manner in which I cook. See, I heat the pan to about 350 and pull it off the fire, by the time I put the butter in the temp drops to under 250 degrees -which is all the heat you need to get the eggs to begin to coagulate.
The net-net is that if you don't have an IR (frankly, I mostly only use mine when I'm studying or teaching) just heat the pan so that when the butter goes in it melts slowly, bubbles but does not brown. Oils are another story for another time.
BTW If the heat is cranked the temp of the pan can exceed 600 degrees F! When you consider that whites coagulate at about 140 degrees, and that browning in eggs occurs at about 325 degrees, it's easy to understand why that is way too hot.
I'll eventually figure out how to elevate the qualities of these things, in the meantime I hope this makes sense!