Elegant Objects by Yegor Bugayenko actually argues against mutation in OOP for the same reasons that FP advocates due (bad for concurrency, hard to test, hidden state is hard to keep in your head, et cetera), but then all you get are namespaces with functions that act on a (usually) single data type (i.e. the class itself and its properties).

OOP itself could be good for problems where you need state machines. The Erlang Actor model is successful for a reason, but I wouldn't apply OTP to general programming.