The problem with "leaky" encapsulation as you put it, is the combinational explosion of the state space as many stateful objects are composed.
Most mainatream programming languages are still unfortunately not well geared up for working with immutable data, they lack even persistent collections. Functional languages are of course ideal for this.
I don’t think it has to be necessarily more than with an immutable approach. Like, there is an essential amount of state you will have to have either case and it is not clear to me that immutability is always the better choice.
But don’t get me wrong, I also default to immutable data structures, I’m just saying that 1) OOP is not incompatible with FP 2) not every problem is solved better with FP-idioms. It’s not accidental that haskell has state monads as well.
There is no getting away from essential state, from a theoretical point of view. In my opinion the often leaky partial encapsulation of state is still one of the better ways to deal with it. And immutability is another axis so of course the frequent case where it makes sense should be adhered to, but not religiously.