They don't have to sue, they just have to send a letter to the new firm. Or even worse the new firm just has to ask "did you sign a non-compete?"
This is the reason why employers ask if you've signed a non-complete
I suppose I was lucky that the new company tried to negotiate a bit, but when my former employer refused to budge, they backed out. My lawyer had warned me that this could happen even before I accepted the job offer, right after he assured me that I would be on solid legal ground in taking the job. Admittedly, I didn't really think it would happen because why would they want to be known as the kind of company that does that? Even so, I've never regretted my decision to leave. As stressful as that was, staying would have been worse.
Non-competes really only matter for people with exceptional knowledge of something.
From a business standpoint, the legal resources to build a case against a single “average person” who signs a generic non-compete are not a good investment.
But like I said, it’s a judgement call. Anyone in the possession of that exceptional knowledge should be able to determine the risk.
So who are the non-competes really for then?
They're for assuaging the corporate leadership that they are actually effective at managing that pesky turnover problem they've been having in a manner that doesn't require them to increase pay or improve working conditions. That and people who carry a "book of business" (the sales team) and those with critical expertise in certain, niche knowledge domains.
There was also an issue that resulted in state legal action where fast food workers were blackballed due to non-competes.