Doesn't work in my experience. I started not too long ago at a startup whose founder actively publicly campaigns against non-competes. Yet there was still a non-compete in my employment contract, and they wouldn't let me strike it, presumably due to pressure from their lawyers regarding potential investors.
They have laudably since removed the clause, even retroactively from current employees' contracts, but it just goes to show how little bargaining power employees have in the arena of employment contracts.
Investors and banks are the root of the problem when it comes to non-competes. They insist that companies include these in all employee agreements.
If you live in a state where non-competes are legal, and if you are a job candidate and they refuse to let you strike the non-compete, then push back with the following: If employment is terminated by them and not you, ask them to pay you 100% of your salary during the non-compete duration so you can go on "Gardening leave". If they refuse to do this, then decline the job offer.
Oh, and make sure you state that you need to see everything up-front I will need to sign in the next 6 months as an employee in the offer documentation package. Some ethically-challenged companies wait until you have accepted the offer and hit you with the non-compete and invention agreements on your first day of employment with a "sign or be fired" requirement.
They have laudably since removed the clause, even retroactively from current employees' contracts, but it just goes to show how little bargaining power employees have in the arena of employment contracts.