If the value to be exchanged is "this allows you to be employed by us" then you should easily be able to rescind your consent and return the value offered by the counterparty. If I am no longer employed by a company, the right to work for them is worthless to me, so I can return it to get back my right to work for other companies.

In order to be enforceable, the non-compete has to pay you just compensation for every week that you honor it. And in order to discourage people from simply rescinding when they quit, it needs to provide tangible value at signing, value that would have to be returned in order to rescind.

For instance: If you sign this, we will give you $2000 now, and your full salary for each of the first 52 weeks after you leave us, provided you do not go to work for one of our competitors (list of specific competitor companies incorporated by reference) during that time. We can rescind at any time, and any ongoing payments will stop after two weeks. You can rescind by returning the $2000, and any ongoing payments will stop immediately.

That's a non-compete with teeth, because it recognizes that the ability to work for other companies has value, and gives other value in exchange for that value.

If BS non-competes are to become more common, notices of rescission might become more common with the resignation letter. Had the subject of the article offered such a rescission notice, she would have been able to sue her former employer for defaming her to her new employer. Now, she would first have to sue for declaratory judgment that the non-compete did not constitute an enforceable contract from the beginning, and then also prove that the old employer should have known that it was unenforceable when they contacted her new employer. That's a lot more difficult than "they told a lie and it got me fired."