The Bible seems to allow polygamy. Why doesn't the church?

In [Exodus 21:10](http://www.biblegateway.com/passage/?search=Exodus%2021:10&version=KJV) and [Deuteronomy 21:15-16](http://www.biblegateway.com/passage/?search=Deuteronomy%2021:15-16&version=NIV) (among many other passages), it talks about polygamy as if it were acceptable. Indeed, there are several holy men (Abraham and Solomon come to mind offhand) that had multiple wives. It seems pretty clear that God doesn't mind polygamy and that it is allowed. Why is there a modern-day restriction on such practices? **Edit**
As has been pointed out, I'm using "polygamy" in the modern/popular sense (such as "polygamy camps" of the FLDS group). Truly, the actual word is "polygyny", which is a man marrying multiple wives. Other forms of polygamy (polyandry and such) seem pretty clearly against God's word. **Edit 2**
Per a comment, I'm seeking any answer from any denomination/doctrine that does not support polygamy. Although there are a few denominations that do, I'm not interested in their history so much.