My supposition about the necessity of ground rules is precisely as supported as the alternatives offered in this discussion. Poorly supported by the standards of rigorous debate, I agree, but supported enough for casual discussion. No one has offered any evidence CoCs are caused by busybodies. ("Silently" seems unnecessary, it wasn't silent, I stated it aloud and described why I thought it was so. I can't help but point out again, you go on to dispute it, but not with any evidence. I think that's fine for casual discussion, but it's not meeting the bar you're setting.)
"Scheme to elevate property values" is a shared interest if all of the homeowners primarily view their homes as financial instruments. People get bent out of shape with HOAs because they want their home for other things. Some people would rather put up radio towers or paint their house a garish color or park a truck on their lawn than maximize their property value.
CoCs are as old as dirt. I signed one every single year in elementary school, decades ago. They've been a norm in workplaces for a long time. They're more recent in open source projects, and they started because of problems projects were having - people being creepy at conferences, people starting drama on mailing lists, etc.
What's recent is the politicization of CoCs.
If it helps, I would agree that busybodies might abuse both of these mechanisms to impose themselves on their neighbors and colleagues. I disagree that that is the root of why they exist, on the basis that they can be explained by incentives and pragmatic considerations. On an Occam's razor basis, if I don't need to assume busybodies are the motivating force to explain the existence of these things, then I won't, until such a time I receive evidence I can't explain without them. Were we colleagues, and I were involved in drafting a CoC, "I don't want a CoC because I'm worried it will be abused by busybodies" is a concern I'd take seriously.