One of the most important aspects of functional programming is immutable data structures, better known as values. Updating these structures using the copy-on-write approach is very inefficient, and this is the reason why persistent data structures were created.
On the other hand, JSON is a lightweight, text-based, language-independent data interchange format. It's become so popular due to its simplicity. There are a lot of libraries out there to work with JSON in the JVM ecosystem; however, none of them use persistent data structures.