I think the main reason churches have been used is that they have big rooms which aren't in use during the weekday, whereas with schools and government buildings you're displacing the people who would normally be in that place.
There's also a bunch of old ladies, who know where everything is and are available to help, in most churches. At least that's true of the (accessible and progressive) UCC church I grew up in, which is still a polling place. With cookies and percolator coffee.
That said, I've voted by mail for decades because it's just easier, especially since I'm filling out both my ballot and that of my quadriplegic spouse. Under their guidance of course.