Sheesh.
And what would they threaten you with? Bring that lawsuit before a judge and they'd laugh you out of the building.
They'd probably have their corporate lawyer write a mean sounding letter, you'd ignore, no way anything happens beyond that.
If you get stabbed don't the police arrest the person and, the state try and convict them? They don't leave it to the victim to mount a case, surely?
A proper legal system would provide sufficient reward to make it always worthwhile to challenge companies _clearly_ abusing their power in that way.
And even criminal trials end up in plea bargain settlements. The trial and deliberation isn't necessarily expected.
For the individual, challenging a non-compete agreement is probably not worth it. But amortising the cost over everyone who benefits it becomes a very reasonable thing to do.
State legislatures have been doing a great job in preventing non-competes from being banned, because they aren't scared of organized political action by labour.
The bigger question is if you really believe that the "laboratories" / Darwinian process of cities and regulations and states and whatever idea in the first place. It's a conjecture by some credible, mainstream public intellectuals. The biggest evidence for it is cities/states accommodating tax avoidance, which so directly affects the bottom line that it's basically an apples-to-oranges comparison with anything less concrete like non-competes.