What you’re describing is the network effect in action, not a flaw in Craigslist.
(It will be the same with every alternative you find, except perhaps one that’s well funded with outside money, which will be awful on the privacy front, of course.)
The way we overcome a network effect is piece by piece:
First we switch to the privacy-friendly service for everything we can. That immediately reduces our exposure, reduces the power of the incumbent, and makes the alternative more useful by giving more users a reason to switch.
Then, over time, we switch for the remaining things as we find a suitable service for each one. (This might even be the same privacy-friendly alternative we started with, after it has grown a little.)
If I felt I had to buy a sports car, and some awful invasive site like Facebook was somehow the only viable venue, I would buy just the car there. I wouldn’t make them the middle man for every other transaction in my life.