The threat of lawsuit is usually enough to get an employment offer rescinded. It’s rare for a company to want to take on a legal defense just to hire someone new. Even though they weren’t actually legally binding, non-competes still limited options for a lot of people.
Overall I agree with you that this isn’t as big of a deal as people make it sound, but it’s easy underestimate their influence if only looking at the result of cases that go to trial. In many situations, the damage is done well before a case can go to trial.