The images themselves may not be subject to copyright, but you can still enter into a contract that says you won’t use generated images without paying for them.
You can’t because copyright law supersedes contract law and copyright law states that such rights are exclusive - thus contract law cannot be used to usurp or invent a copying restriction. Licensing is the exclusive right of the copyright owner and when no copyright exists there can be no license (or de facto equivalent).
It’s not though, it’s a restriction on using the material produced by the service. Any contract terms regarding such are superseded by copyright law - the only rights belonging to the owner are those granted by copyright law and the only restrictions that may be placed are those that copyright law permits.
No, the rights are not superseded by copyright law. Why do you think that? Your agreement with the service provider is just like any other contractual agreement. Should you use one of the generated images (that you generated and used outside the terms of your agreement), you would not be sued for copyright infringement. You would be sued for breach of contract.
What you're saying is akin to signing an NDA, violating it, and then saying your First Amendment right supersedes the NDA. It doesn't.
It’s been federal law since 1976 that copyright “preempts” any other laws granting overlapping claims. This includes contracts, which fall under state law. Now, strictly speaking the courts are divided on how to treat the specifics of these issues with respect to EULAs, but the Genius vs Google case should leave one weary: