At least at US restaurants, a "small" omelette is three eggs and larger ones more, though. And likewise for servings of scrambled eggs. Pretty much the only case where 1 or 2 eggs are the norm is when ordering fried eggs (and those are generally accompanied by bacon, potatoes, toast, etc.)
There might be longterm malnutrition problems if you’re solely eating eggs in mass quantities (since 20 eggs for a 50 kilo person would be hitting near your daily caloric intake just in eggs), but for most people this isn’t a concern.
Having 5 eggs for breakfast (not as an omelette, which obviously has other stuff in it) every day would probably improve most people’s health.
