I think a too easy reproduction mechanism means not evolving intelligence. The selective pressure for human intelligence could not have came from the environment or else many species would be similarly intelligent like how many species can fly. It was some sort of a competition inside our species, probably sexual. And when reproduction is easy, sexual competition is not so tight. In fact, the most likely answer is that the runaway explosion of intelligence that resulted in us must be probably a mutually reinforcing process: intelligence made reproduction harder, hence more sexual competition, hence more pressure for intelligence.

How did intelligence make reproduction harder? Through big heads making childbirth harder. Frankly I don't know why didn't evolution just came up with the idea of giving women gigantic hips and large vaginas, but what happened instead is that babies are born far too prematurely so that their head size is not too big, and thus require a huge amount of care and investment after birth. This, postnatal maternal investment, then intensified sexual competition and thus pressure for more intelligence.

This really rules out the external eggs.