Although that explanation makes intuitive sense, it seems to be based on a massive overestimation of the amount of H2O that currently exists on Earth. A thin layer of water covering two thirds of the surface is not much compared to the entire mass of the Earth.

Isn't it possible that early Earth contained many times as much H2O as it does now (like some of those Jovian satellites that are covered in hundreds of miles of ice), and what we have now is simply what's left after the majority "boiled off"? That way, there would be no need for comets and asteroids to return the lost water to Earth.

Other comments in this thread mention vast amounts of water trapped deep inside the Earth, as well as outgassing of nitrogen after the Earth has cooled down. Perhaps the water near the surface of the early Earth did "boil off" entirely, but what we have now is the result of subsequent outgassing?