P51, while I also dislike the form (IMO it's wordy, confusing to a layperson, poorly drafted and overreaching in many respects (e.g., "save harmless....") and has other defects including typos, I think the reason you may include explicit discussion of who gets to register the copyright is to preclude any argument by model of joint authorship. I assume it's driving at that otherwise I don't know what the heck it is doing in there either.
From the statute: A “joint work” is a work prepared by two or more authors with the intention that their contributions be merged into inseparable or interdependent parts of a unitary whole.
Though I don't understand the language in the that particular agreement. You don't really want or need permission to register the copyright you want a statement defeating any argument of joint authorship.
It's not an issue if doing, for example, a portrait. But I could see a situation where you hire a model to explore different ideas and the model contributes ideas and creative input to the creation of the image. There is no blanket prohibition against a photographic model asserting a claim for joint authorship.
PS, thank you for your note. I'm digesting it.