If you sign a contract in bad faith, then you are in principle not agreeing to the contract, as you are not abiding by the essentialia of the agreement. Which is that both parties must willfully agree to the terms, and sign it bona fide.
Cute theory. The problem with that is that the burden of proof is with the ones questioning the bad faith. Good luck with that.
People would admit bad faith to friends, family and/or close workers, not in writing to their boss or HR.
Non-compete clauses are there specifically to protect the employer, to prevent employees from stealing their ideas or clients and setting up shop in the same jurisdiction as the employer's area of business. If you sign a non-compete in bad faith, then it means you have the intention perhaps in future to do exactly that. Steal their business.
No. If that protection comes at the expense of another (constitutional) right then there might be the case where such protection is in conflict with other rights and therefore unenforceable.
I have to ask: have you ever read any non compete from pretty much any big company in, say, Europe? If you were to follow them to the letter, after you leave (voluntarily or not), you can't work for any supplier, service provider or competitor, past or present, for a period of 2-5 years in every jurisdiction the company does business in or with. People from companies like unilever, phillips, abi, diageo, nestle, ge, lvmh or p&g (big companies, global reach, tens of thousands of suppliers/etc) would be basically unemployable anywhere if you enforce those contracts. That's why they dont stick and are not pursued legally.
People tend to become specialists and that means that there is a strong chance you will stick to a specific field/industry (IT and HR tend to be exceptions to this). Even in generic things like finance, it's strange to find someone who specialized in consumer goods switching to commodities or mining. Happens but it hardly the norm. You become a specialist and that's what allows you to bring value to the table. Saying you cant work in the industry anymore (as it would mean working for the competition) is seen as a limit to your right to work in quite a few jurisdictions.
I know people who signed non competes and then moved from unilever to p&g, from nike to adidas, from puma to UA, from diageo to abi, from heineken to diageo. Not one of them was called out on their non compete. Not one. And when you ask "why?" they all tell you the same: it's expensive and odds are you will lose.
Unless it's someone very high up and with very specific knowledge or you can take clients away, they are virtually unenforceable.
PS: Just imagine if rugby players were asked to sign non competes.