No. “Sectarianism” is just a convenient, comforting excuse for the fact that Obama has done nothing to stop AQ and its offshoots from gaining one victory after another. Having three or more even weaker smaller states certainly wouldn’t help; in any case, all of these places would have minorities of the other sect, so even if “sectarianism” were the problem, that wouldn’t help. And they would have had their allies in the larger states governed by their particular sect (Iran, anybody?), who would certainly not have been content with the measly little patch of territory their adherents had.
The only thing that would have helped would have been the establishment of a strong civil state governed by the rule of law, which was what we were attempting to do and nearly had done by 2009 - when Obama threw it all away by dumping Iraq. The civil government wasn’t strong enough, the economy wasn’t strong enough, and their military wasn’t strong enough.
A strong, stable, modern Iraq would have served as a barrier to AQ and Iran alike, which was the point of the whole exercise.
A strong, stable modern Iran would have prevented this all to start with.
Thanks, Jimmy Carter.