You can definitely fry eggs on teflon without butter or oil or anything. I have this vague memory that I used to be able to do this on cast iron when I lived in the US, with maybe the occasional bit sticking.

You can do this to a brand new, high quality teflon pan, but it will gradually become less and less possible as you use it more.

But why.

Well, if one really wants to taste the subtle tastes of an egg, cooking sans oil does that.

By subtle, I mean similar to the difference between veggie oil and olive or canola oil. These all have a distinct taste to me, and I dislike canola enough to notice when it's been used.

The egg by itself has flavors that get dominated by the oil flavors.

To some people it matters. Simple as that.

Many people abhor chicken fried in canola oil.

Great! I can't blame them. It is terrible.