Eggs are dense little packets of excellent nutrition. They have good cook and relatively cheap. While it's true the egg yolk contains all of the egg's fat, it doesn't mean you should switch to eating egg white omelettes.
As well as all the fat, the yolk contains two-thirds of the egg's protein. Plus it's in the yolk where you'll find the majority of the vitamins, minerals and antioxidants, nutrients like calcium, iron, zinc and folate, as well as vitamins A and E.
It contrast, the egg white has small amounts of B vitamins and potassium, a measly one-third of the total protein, and that's about it. So stick to eating the whole egg, and you'll get all the goodness at once.