Thank you. 
I also find cosmological arguments unsatisfying, but I don’t think that is a circular argument of the type I described. The interpretation (as I understand it) is not based on probability, but rather possibility or even mathematical inevitability; there is nothing in the mathematics to prevent it from happening**. That said, it doesn’t rise to the level of theory until someone finds a way to test it.
** To my mind the Copenhagen Interpretation is reasonable when viewed as possible futures (like a probability distribution) only one of which is realized. I find it harder to accept as multiple realized futures - but that’s how some physicists see it.