It's a fun notion, but it doesn't account for historical realities. Nor does it acknowledge the minor point that for a substantial period of time the Muslim world was a much nicer place to be than Christendom.
That's the bit I don't get. We recently learned about that in history, and all I could think was, what the hell happened?
The same thing that happened to the christian kingdoms soon after the collapse of Rome: religious fundementalism. Suddenly new ideas weren't tolerated, especially non literal interpretations of holy texts. Islam is still in a Dark Age, and unfortunately I dont see the light at the end of the tunnel (yet). The biggest problem at the moment was Saudi Arabia, their petro dollars have been financing the spread of radical islam for several decades now with no end in sight.