I don’t think this is true. You can always request changes in the contract, and you should consider it. It may seem expensive, but worth it, if you have the money to have your own lawyer read your contract and propose modifications that suit you. It may also reveal to you that parts of your contract were unenforceable.
In my experience, it hasn’t hurt me or anyone I know who’s negotiated their contract. In some cases, because it’s somewhat rare for people to negotiate the non-compete terms, it made me look more confident and desirable than other candidates.
BTW, there is no reason you can’t do this long after being hired and after signing your employment agreement. Companies and lawyers can and do make addenda after the fact all the time.