While the world can tentatively be conceived to be like that, it is not nearly "just as easily". Lots of those "immutable facts" can't be realistically discovered: e.g. good luck recovering "this blackboard had a drawing of a cat and a bird until five minutes ago when it was cleared with a wet sponge" if you weren't there in time. The approach with mutable state fosters this destructible nature of many things upon you and makes you cope with it, somehow.
Ok, but why should I even care about what was on this hypothetical blackboard? Do you have any real world examples with business or technical significance where this "cope with it, somehow" approach to mutability is a clear win?
You've just stated it, no? If you only care what is on that blackboard right now, not what was there — why even bother storing knowledge about its previous states?