Would it really be that interesting if the US were named so symmetrically? The "Atlantic Northeast" is referred to as New England because it was heavily settled by people from England, and it was their new home so they called it, oh my gosh, New England. It's really no different than New Jersey, New Amsterdam/York, New Hampshire, or any "new" geographic names.

As for the Midwest, it was once called the Northwest because when the US was young and relatively small (pre Louisiana Purchase, 1803) Ohio, Indiana, and Illinois were the northwest. Congressmen from these young wippersnapper states were called warhawks in the war of 1812 because they wanted to experience a war like their fathers got to in the Revolutionary war. Yes, these new western states were represented by young, immature politicians. But anyway, when the Louisiana Purchase was made, this area became known as the Old Northwest, because it was no longer the northwest. I would assume that when these states became the middle of the US, they wanted to retain the "west" so they took the moniker "Midwest".