Aside from the reasons we've discussed already, which are good, I stumbled across another explanation: the churches have become people of the lie... (0 - 3:30 min)
Ran across this video and although his subject is completely unrelated to this subject, his first 2.5 to 3.5 minutes were spot on in describing the mindset that may be behind this. Its a brilliant description of what happens when people embrace a lie.
This also leads me to a possible explanation of the why of the reaction. The push back against homosexual marriage by the church caused them to identify with one man and one woman only. In reaction to one lie, they absorbed another and made it a core part of their identity. On top of that you have their revulsion at the thought of anything that causes women feel-bads and their steadfast defense of women's efforts to subtly rule their marriages; two things that polygamy overthrows.
The embrace of lies about women are wrapped up in there somewhere too. But I didn't live through those changes in the church (likely around the 60's when headcoverings were dropped) so I can't put my finger on how that played out.
This is why I said elsewhere you can't lead with polygamy, you have to strike at the root of the problem. If they think causing women feel-bads is mortal sin, you'll never get them to even consider polygamy as it is de facto sin by that measure alone.