Right, the standard contract term is called 'consideration', meaning that for a contract to be valid and enforceable, each side must be giving up something of value as part of the transaction.
This is simply not true. It has nothing to do with at-will employment. It is state law. Some states require consideration separate from salary, some say continued employment is sufficient consideration. 49 out of 50 states recognize the doctrine of at-will employment. Only Montana uses just-cause instead (just like the rest of the developed world coincidentally).