I wonder how close to blasphemous it would be to say that's a pretty appropriate meme.
Too late, I suppose, saying it was a pretty good description seems to put me in the category of getting to find out.
One problem with monothelitism is that it had some enemies that worked vigorously to see it abolished. Sts. Sophronius and Maximus the Confessor come to mind, as well as most of the Popes during the controversy. Most of them would have to be neutralized for this doctrine to take root, and that would be tricky. This might heal the Schism between Eastern Chalcedonians and Miaphysites, but it would sunder relations with the West for good. I think any significant change in the religious fabric of the Mediterranean world would butterfly away Islam, though.
I was under the impression that early on, the Popes were employees of the Eastern Emperor and with the waning of the Byzantines, they were threatened by the Lombards and sought the help of the Franks to deal with this.
I'm not familiar with the timeline of Monothelitism though--how strong were the Byzantines in Italy? If they were very strong, they could simply sack a recalcitrant Pope. If not, they might need more subtle means.