Would having a couple of boiled eggs with a class of water be enough for a great breakfast?

No it wouldn't because it doesn't contain all the classes of food
Whereas egg as a protein can keep you fuller than other classes of food; you still require other food types like carbohydrates and fibre to keep you going

I’m not that much of a breakfast person, but if I do eat breakfast, I’ll typically eat something like that. It depends on how you feel after eating breakfast, how much it affects your energy levels, etc.