I'd add that "waters" doesn't need to mean more than one body of water. It can be used somewhat poetically to refer to water in a single body. First example I could find: https://biblehub.com/joshua/3-8.htm
In tree leaves, it could be leaves from a single tree or multiple trees. Hence, you can't pluralize tree into trees leaves, tree isn't allowed to recieve a plural there. If you write it as tree's leaves, then tree is singular, and the form is possessive (whereas before it served to disambiguate from, say, leaves of a book). Then you can also pluralize tree to trees' leaves, and now it's leaves from multiple trees.
Hadn't even considered that. I think that confirms "waters edge" can be grammatically correct. (random example: "as rain falls, flood waters edge closer")
Yeah, that could totally be by design. For example,the book "Rainbows End" is not "Rainbow's End" specifically because the meaning of the first is intended, not the second.
In the book's context. But in the meta-context of why it's in the book, the author's intent is to fool you into thinking it's a mistake, when it actually isn't. Specifically, it's supposed to suggest the technological singularity not being a pot of gold but the death of history (and possibly humanity).
But hey, there are no rules or logic in English so have at it!