If I signed a contract stating that I was supposed to name my next child "Bob", they could try and sue me for violating that contract as well.... that doesn't mean that I'd actually end up owing them anything. A contract that requires you to do things that a company is not legally allowed to ask you to do is not enforceable. It should go without saying, even though it is usually made explicit in a non-compete contract and is true anyways even if you never sign one, is that you are not allowed to disclose any confidential knowledge or proprietary information to other parties, and in places where such contracts are actually legally enforceable, an actual non-compete can at most only prohibit you from utilizing your former position in the company to harm the company, where it is important to realize that hypothetical harm does not actually amount to harm... the fact that you could face civil damages for doing so is going to generally going to be understood by a judge as incentive for you to not do such a thing, and in absence of any evidence that they may have which suggests that you did (which they would not have if you did not do so), they would not be able to convince a judge that you owed them anything... the fact that you may have lied about the detail in the contract gives them no more legal claim to damages than it would be, again, if they had required you to name your next child after your boss and you didn't.
That said, I'll certainly agree that it's sort of pointless to sign contracts you don't intend to abide by, even if aspects of the contract are not enforceable, because doing so can still potentially damage your credibility, if that is worth anything to you... but in my experience with non-competes, it will never be worth a company's time to ever even go after you just because you might happen to work for a competitor unless you have actually used your former position in that company to harm your previous company in some way (which in many cases, depending upon your former position with the company, you may be able to accomplish with equal efficacy without having any employer afterwards at all, since they cannot generally prohibit you from simply communicating with whomever you like when you are not within the company, unless said communication would also entail a violation of criminal law in some way, which may be entirely theoretically possible, and would not just carry civil penalties anyways, and if such were the case, then it would be equally true even if you had not signed the non-compete at all).