Why and when did the U.S. make such a policy?
Around 1877-ish, with "Wood's Rule".

It seems so unconstitutional
What part of the Constitution do you imagine the Doctrine of At Will violates?

Don't other countries make At-Will termination policies illegal?
Some do, some don't. Who cares? We deal in US law here.

As Betty notes, At Will goes both ways. If your employer sucks, you can leave without notice or legal repercussions.