Because the Egg Gods and the Odds Gods prefer to hear the "per egg". It makes them more merciful to us breeders when the tiny heads start poking out of each egg.

That's my excuse.

The coin flip explanation is a good one too. And it's true that it 'seems' like the 50/50 clutch would be true in the 'real world' but using the same math to figure a multiple gene clutch will lead you to possible disappointment, since if each egg has only a 1/16 chance of being your golden combo, just because you have 16 eggs doesn't mean that you'll automatically expect at least one of the golden combo. Since each EGG has a very small chance of nabbing all the genes it needs, it's a less likely outcome than just needing to produce 16 possibilities/eggs.

On the surface, it seems the same thing egg vs clutch. But it really does make sense once you delve deeply into it.