And why would ad copy not by copyrightable? I don't see a creative commons license at the bottom of craigslist ads.
I'm not sure where all this entitlement comes from that you think you have a right to another company's database simply because it's index is public.
If Craigslist changes its name or sells its SF apartment listings to some site with a name you do not like, what can you do? Answer: Nothing, because you gave them an exclusive nonrevocable license to your data. If you really wanted control over your personally identifiable data then it would probably be wise not to submit it to a site that gets scraped and cached by Google (from which anyone can make fair use) and certainly not under a license that gave you no control over the data after it's submitted. You would want a site that has some sort of protections like passwords, that allows some degree of pseudo anonymity so your name is not embedded in an evergreen search engine cache; and you would want the right to tell the site to remove/delete the data at your direction, if that became necessary (e.g. in your example scenario).
In short, Craigslist really isn't in the business of protecting your data for you. Its terms are what they are because it's seeking to protect its own business, which relies on your data.
The users know CL is sharing it with the world and that's what the users expect. As the article says, CL is happy for search engines to access these. Just obviously not search engines that they don't like.
You don't get to pick and choose who accesses your website unless you put a password up. And if the content's not copyrightable...