An alarming number of "moderate Muslims" DO want Sharia law actually. 

According to a 2007 poll conducted by the PolicyExchange think tank in Britain, nearly 60% said they would prefer to live under British law, while 37% of 16- to 24-year-olds said they would prefer sharia law, against 17% of those over 55. Also 36% of 16- to 24-year-olds British Muslims believed that those converting to another religion should be executed. Less than a fifth of those over 55 think so

30-40% of a Muslims wanting it isn't insignificant, and as we've seen in Muslim majority countries, the "moderates" don't do anything to stop it from happening. While the "radicals" throw gays off of rooftops, the "moderates" watch from the street.

Look at the actual data:

https://en.wikipedia.org/wiki/Muslim_attitudes_toward_terrorism