Most contracts with a notice period still allow the company to just pay it out and send you home on the spot.
You even have a contract when you are buying a piece of candy at the newsstand.
(At least in the common law world. In eg German law technically you have one contract for the piece of candy, and one contract for each individual coin you are handing over. See https://en.wikipedia.org/wiki/Abstraction_principle_(law) Germans are a bit crazy.)
> At-will employment is a term used in U.S. labor law for contractual relationships [...]
Emphasis on contractual.
Or am I missing something?
A contract that can be dissolved at will is still a contract. Just like you can cancel your Netflix subscription at will, and it's still a valid legal contract.