GUI has been one of the strongholds of mutation-encouraging paradigms though. It should be said. I would use it as an example, where one probably might need mutation for performance reason and for the reason, that I find it a bit too overheady to create a new widget for every small change. I don't know enough about how some languages try to solve this and stay declarative or functional, to comment on that.
if you believe in super-determinism and that everything progresses based on predetermined laws you can take the view that space+time already exists in all its past and future and that nothing happens.
or, quantum mechanics in the multiple world interpretations. you can say that the state of the world literally splits whenever there is an event.
i guess the metapoint here is that just because something seems mutable does not mean it’s really mutable and that mutable and immutable only make sense at certain levels of matter organization (are atoms mutable? what about photons? what about quarks?)
Rich Hickey (Clojure creator) himself has a similar, interesting, and compelling take on time and mutability [0]. This perspective is the underlying basis of Datomic.