I think the issue is the ToU violation, not copyright.

Violating a ToU is legal, but the corporation might ban you in return because that's legal too. All you give up is your ostensible right not to be banned.

Don't terms of use depend entirely on copyright to work? Without copyright ... why would you need to agree to terms of use to use the software/site/data?

And doesn't that mean that terms of use can never impose restrictions stricter than copyright?

No. ToU is a part of contract law. Basically the website is providing a service for you. In exchange for your use of that service, you agree to be bound by the terms. This implicitly creates a contract between you and the website, with the terms laid out by the ToU. This sort of implicit contract is legally controversial - normally for a contract to be valid there needs to be affirmative signatures from both parties, as well as consideration (money) exchanged. In the U.S. at least, "click-wrap" (where you must affirmatively click "I agree") and "scroll-wrap" (where you must scroll through the whole ToU before the product unlocks) ToUs are generally considered enforceable, but "sign-in wrap" (where creating an account binds you) and "browse-wrap" (where there's a ToU link) are very dubiously enforceable. But we're talking about Google here, and they make you click through the ToU and say you agree whenever you unbox a new Android device or create a Google account, and then have it apply to all usage of Google services.

Enforcement can be quite challenging because typically if you provide a service over the Internet you don't have any idea who is using it beyond their IP address and any registration data they provide, but this also means that when companies do have a known violator and can show significant monetary damages, their legal departments come down like a ton of bricks.