Other than wanting an IP that's not directly tied to you?
If your crime is downloading Frozen, and the authorities can’t find any trace of the movie on the device the logs claim was used, then it would be shameful if the logs alone were enough to convict the person.
If you have a server, allocated an IP, and someone sees that IP... that's a pretty direct tie.
Not if you pay with cash (such as Mullvad). Then it depends on what they can infer from your traffic.