I do not know why not. It is a place where they have the room to do it. It is a place where they have the parking and people that can volunteer to help. It is not being influenced by being there. In fact it might even provide a safe place for people to vote in some instances.
There are loads of businesses/establishments where voting occurs without promoting their products or point of views. I don't think there's any reason to exclude churches as long as they do not use it as an opportunity to promote their faith. Earlier today, I watched a clip of some of the strangest polling places in the U.S. Among them were a mortuary, a laundry mat, and a beach! Point being, there are many different types of polling places, and there is no reason to exclude churches.
I don't see why churches shouldn't be used as polling places. There is nothing inherently biased about a church. Sure, they are statistically likely to be biased in one way or another, which may change over time, but so is every other place. Libraries are used commonly as polling places, although I'm sure a study would show that on average, librarians tend to relate to one political party over the other.
However, there's nothing we can do since these polling places are by nature comprised of the people within, which are not robots and are going to have their own opinions. Thus, legally they are not allowed to let those influence people on voting days.
It's been shown that people who vote in places of worship often feel pressured to vote against things like stem cell research and abortion. A voting location should be neutral territory where everyone feels free to express their opinion in the way they vote. We should be using public libraries, post offices, empty properties in the neighborhood over houses of worship.
Churches already brainwash their followers to think what they want them to think as it is, they don't need to be allowed to tell them who to vote for too, one mind manipulation is more than enough. So no I don't believe churches should be used as polling places, they already control your thinking plenty to begin with.
I personally feel that we should avoid using churches as polling places simply to avoid any potential problems that could arise in regard to the separation of church and state. There are so many alternative polling locations that are available, that there is really no reason to utilize religious institutions as polling places.