How does that help? If you're the only one with traffic from that IP, how does that give any privacy? Especially if you pay with something tied to your identity. And why does a VPS have any less likelihood of logging your traffic?
Then don't do that.
Though VPN are not really a strong solution for hiding your identity period. Tor is a more effective tool, but hiding your identity is extremely difficult to do effectively.
> And why does a VPS have any less likelihood of logging your traffic?
They may be too but at least you should expect their business to be viable without doing that, which is better than you can say for VPN services.
You'll be stuck with the shadiest, slowest, most remote VPS in the world if you're unwilling to either give up your personal identity, or lie about it.