Worth noting that employers can still try to enforce it via sending nasty-grams to your new employer, which can definitely cause you significant issues if your new employer isn't willing to take on the risk of being involved in a non-compete lawsuit on your behalf.
The key thing is that if your old employer is sending out demand letters, you have to go through expensive legal proceedings to clear the encumbrance on employing you. Your new employer has a letter stating that they have to either immediately terminate your employment or get sued - even if they will win in the eventually legal proceedings, lots of places are not willing to get sued over it. Some won't even be willing to pay a lawyer to figure out whether or not the suit has merit.