You're talking about "severability" in US contract law. The rest of the contract was either stupid (regulating my usage of the non-existent golf course) or just garden variety stuff (can't sublet, etc.).

The same company also just dropped off an "updated" contract a few months later and told me that I had to review it and sign it or move out by the end of the month. I obviously just ignored this.

Right, but in an employment contract you want that severability. If the company tries to enforce the non compete clause and it’s invalid, you don’t want that to invalidate their obligations with respect to your pension.

My experience with companies pulling DIY contract addendums out of their ass is that they forget severability clauses. Or that the contract starts falling apart because they have other sections which refer to the severed part which means those sections also fall apart. For example, a damages section that ends up exceeding state law.

DIY contracts are the best to sign because they are such a mess.