Of course, occupation is not guaranteed to work. History tends to roughly repeat itself, but no situation happened twice. Every situation is different somehow, we can speculate and deduce from past experiences, but we can't have certainty. Germany and Japan are not perfect examples, but they are valid arguments. I can't really find a case where a more primitive country was occupied for a long time and whether it brought results or not. Both Germans and Japanese think differently than people in the Middle East. Still, Japan had Western mentality successfully imposed on them (for Germany, the jump wasn't nearly as big). On the other hand, their honor system means that, as the defeated side, they had to agree to that. Arabs may be less susceptible. This is compounded by the fact Japan had no religious issues, Shinto is permissive of other faiths and religion in general plays a different role in Japanese society (Islam, on the other hand, is very "intrusive", with a multitude of strict rules, mandatory daily prayers and very little leeway for its believers). On yet another approach, Japan was technologically on par with America, Middle East is not. If the West was willing to invest in the region, it could greatly improve the quality of life there, possibly inclining people to warm up to the occupation.
I think that occupation is our best chance, strategically speaking, and a better choice than destroying the region. However, there's also an economic consideration. Occupations cost money. I have doubts on whether capturing the oil fields would recoup the cost. Likely not. The economic situation in Europe is sticky, and the US isn't doing as well as it'd like to, either. We're looking at over 20 years of supporting an occupying force, along with improving quality of life in the region and generally trying to keep it working. Being unable to pay for something doesn't usually stop politicians from doing it, but it seems that since the latest recession, everyone started to watch their money. This is part of the reason why I supported just exterminating the IS (especially earlier, when the economy was even worse). It's the cheaper option, to put it bluntly.
The way I see it, we have two semi-decent options. Occupation and destruction. NATO doesn't have money for the former and public support for the latter. It also doesn't have balls for either. So we're implementing a half-arsed solution and hoping that the region will sort itself out. I can't see anything good coming out of that. I just hope the Jewish Quarter in my city stays off their radar (it's mostly a historic site, there are a few Jews around, but hopefully not enough to warrant blowing it up).