I agree that when it hits the news it's generally a lawsuit against a VP, but you have no idea how many times lawyers send nasty letters, which are pretty effective.
Yep, letters cost almost nothing to send. Almost all employees have nothing to worry about for one reason. The corp will not go ahead with a lawsuit because the employee will almost always have no money or assets to take. It's amazing how pathological corporate behavior becomes when one views it from the money perspective.
But there's a chilling effect. For lots of potential employers, the existence of a non-compete that might be litigated is a complete non-starter. I worked for a small company and I know for a fact we passed on at least one person who had a non-compete that was unlikely to be litigated but it just wasn't worth the risk.