The fact that he can be as successful as he is says much about the USA. Comics are overwhelmingly politically correct in that country, just like they are here in Australia. However there is a much stronger tradition of free speech there. Also, the entertainment industry is more meritocratic. That's why it boasts Miller and quite a few other well known performing artists who openly identify as conservative.
Have a look at that monologue. Can you imagine any well known Aussie stand-up doing something remotely similar? Even a couple of lines with a similar edge would swiftly be deemed "Islamophobic" by the commissars of Artsville and he'd carry the false label "racist" from then on.
This accusation might not end his career. But it would certainly ensure that he was much further down the list when gigs and grants are handed out. No wonder you don't see such material performed here. No wonder, too, that when the subject of Islam is dealt with by comedians, the mockery is overwhelmingly aimed at our alleged intolerance of it.