Well you're not "deep frying" it you're pan frying it. The difference is the amount of food exposed to oil.

For eggs it is about the same, egg's white is thin enough on a skillet and its down side is fully immersed into oil.

This is just not true. Not even if you have a single egg on super large pan. And you can also use smaller pan or more eggs, that way it will be even higher.

Just because you have drowning eggs in oil does not mean everyone does it that way.

Mine take ~ 1 tsp for three eggs. I let the pan get hot enough that it slides around with water like viscosity, spread it evenly with a paper towel and throw the eggs on.

Comment I was replying to meant crispiness. That means frying in oil, in my experience. Do you know another way to get crispy texture on cast iron skillet?

You have a bit of oil under the egg.

I cook exclusively with cast iron pans (not because I’m some sort of purist, but because that’s what I happen to have), and you can absolutely fry an egg with just a bit of butter or oil and no crispiness.