That is the opposite of what I said. Hatching eggs is *faster* than receiving eggs, (at least with Oval Charm and Flame Body). The situation where my party fills up with eggs is primarily in USUM, where the time for the Daycare Lady to receive an egg is longer than SwSh, and I receive them one by one, instead of adding 5 eggs at a time to my party.
I primarily do the first method in SwSh, and the second method in USUM, but I have no idea if I am doing it most efficiently in either game.