What you're describing is called the "Actor model"; in your example, the receiver is an actor that has exclusive control over all bank accounts.
The actor model reaches its limits as soon as you need transactions involving two or more actors (for example, if you need to atomically operate on both the customers actor and the bank accounts actor). Then you can either pull all involved concerns into a single actor, effectively giving up on concurrency, or you can implement a locking protocol on top of the actor messages, which is just mutexes with extra steps.
The actor model reaches its limits as soon as you need transactions involving two or more actors (for example, if you need to atomically operate on both the customers actor and the bank accounts actor). Then you can either pull all involved concerns into a single actor, effectively giving up on concurrency, or you can implement a locking protocol on top of the actor messages, which is just mutexes with extra steps.