You are correct that Mormons seem to have an above-average number of children. It is not uncommon for Mormon families to have lots of children. I live in the Puget Sound area. For non-mormons in this area the norm seems to be 2-3 children. For Mormons in this area the norm is probably in the 4-6 range although there are several families just among my Mormon friends that have 8, 9, or even 10 children. My observation is that Mormon families in the intermountain west (Utah and Idaho)tend to on average have a few more children than say those Mormons in other parts of the U.S. I've also noticed that non-mormon families in Utah have more children than their non-mormon counterparts in other states. So I think part of the answer is cultural. 
 
A decade or two ago - and before - there was gentle counsel from our leaders to not follow the cultural norms and have only just a few children. I don't hear that as much anymore. I think part of that is the economic realities now as compared to the 1950s, 60s, and 70s. 
 
There is a spiritual component to the question as well. The church is, as you probably know, a very big defender of families in general. This is taught very strongly that the family is the foundation. In 1995 the church issued a document called "The Family:A Proclamation to the World". This is a very significant proclamation. It undoubtedly is considered doctrine. Here is a link Proclamation on the Family 
 
Members of the church believe that there are many spirits of Our Heavenly Father that will still come to the earth. We feel and have an obligation to provide a spiritual home on earth for these children to come and live. The more children that can have a nurturing and happy home and family - the better off they will be. So we need to do our part to help them. 
 
The family is the eternal unit for all of Our Heavenly Father's children. It is sacred and holy and must be protected.