Nobody knows. It started in about 900AD in monasteries (because the monks were the only people technical enough to maintain and play one) and became part of church tradition a few centuries later.

And after a millenium of use, in the late 1980s to early 1990s almost all churches stopped using them.

Religion has always had music. An organ is cheaper, and more scalable, than an orchestra to accompany mass, in both small and large settings. And apart from the very rich, churches were the only places that could afford an organ.

My hunch is that only churches were big enough. Also, religion was a major focus of western music, at least as formally sponsored. I have no doubt that there were parallel developments of folk music, but probably using more portable instruments.

Today, tradition. But a lot of churches are using rock bands.

John Calvin would wholeheartedly agree with you.