As far as I know, in a lot of country (like France) it is a legal obligation to keep logs and be able to identify one of your customer if the police demands it. Therefore, if you have server in France or any country with similar rules, you can't operate a "0 log" service. And since those kinds of services have servers everywhere (and it is even one of their selling point), it is extremely unlikely that they don't keep you data and will hand it to the police (willingly or not) if requested.
And if their own server get breached, you can get the info of all the customers who used the breached server.
So I find the claim of those services that they provide "more privacy" pretty lousy. Yes they do hide your IP addresses, but that's far from being the only data use to fingerprint you. And if it is to protect you against a Wi-Fi that you don't trust or your ISP, sure it works, but you move the trust from them to your VPN provider.
Fighting against geofencing is good though.