An IP address is light-years from a real-life identity. Without a warrant, there's not a chance of figuring out even the account holders name-- which could be different from the person who actually performed the transaction. It could be a neighbor, a friend, a roommate, anyone else who ever had the wifi password, the possibilities are endless.
If anonymity is a concern getting a court order doesn't sound like a big deal. Even if not, you vastly overestimate the anonymity an IP provides, and if anonymity is a concern legal deniability isn't a big win either. You also ignore that you could potentially get dozens or hundreds of IP addresses. Anonymity, like security, is hard, and has layers.
Yes, the addresses are public, but there isn't a way to prove who's who according to addresses alone.
Unless of course you publicly attach your identity to one.