I'm trying to read Scholze's article "*Etale cohomology of diamonds*" (arXiv link) and both in this article and in Berkeley notes, the diamonds are defined as sheaves on the category of characteristic $p$ perfectoid spaces that can be written as a quotient of a perfectoid space by a proetale equivalence relation. What I don't understand is that why can't define diamonds over the whole category of perfectoid spaces (or at least perfectoid space over a base $S$).

Are there some important properties of diamonds that only work over characteristic $p$ or is this because we only need diamond in characteristic $p$ case?