Interesting concept. But here's the problem. And this is from someone with a PhD centered in Islamic Studies, not some ill-educated yutz from the New York Times:
Shari'ah (way, path, road in Arabic) has a number of components. Its core is theocratic, that is, those revelations found in the Qur'an that are legalistic. There are about 600 verses that could be considered legalistic with only about 80 specific ones. Thus the Shari'ah also draws from the ahadith (sing. hadith) that are reports of the traditions of the Prophet Muhammad, that is, what he said or did or allowed to be said or done in his presence. The idea here is that Muhammad, being a prophet of God, was most familiar with God's intentions as to how a person should behave himself.
Another component of the Shari'ah are the decisions of religious scholars/jurists made by interpreting the above sources and applying them to the circumstances before them. For the majority of Muslims, the Sunni-s, this ijtihad (original jurisprudence) was stopped in the 10th cen. CE and after that only applied interpretations of these original decisions allowed. For the Shi'ah jurisprudence never stopped and also includes the ahadith of twelve Imams.*
But a fairly large part of the Shari'ah, and something that I think allowed Islam to quickly expand** in the first century and half of its existence, is local tradition modified by and modifying the other parts of the Shari'ah. Thus the Shari'ah in one area is not necessarily the same Shari'ah one would find elsewhere. The result of this can be seen in the extreme example of the various ways adultery is punished in different Islamic countries.
So knowing this, my questions for those calling for the application of the Shari'ah ANYWHERE are:
And who gets to decide?
*This is another lecture.
**By around 710 CE areas under Islamic control stretched from the Pillars of Hercules to the banks of the Indus River.