That kind of demonstrates why XSLT is a bad idea as well though. JSON has its corner cases, but mostly the standard is done. If you want to manipulate it, you write code to do so.
JSON correlates to XML rather than XSLT. As far as I'm aware, XML as a standard is already done as well.
XSLT is more related to frontend frameworks like react. Where XML and JSON are ways of representing state, XSLT and react (or similar) are ways of defining how that state is converted to HTML meant for human consumption.