I love hay!!!!!! But I am also obsessed with gardening....... I put hay in the coop/run, let the chickens eat the weed seeds out of it and add "fertilizer" to it and then haul the used hay to the garden to use as mulch. Works great but fairly labor intensive!!!
I use hay, I clean my coop out once a week though. I scrape it and clean it very good. Where I live hay is very inexpensive, if it wasnt I would switch to something else. I also think it helps keep the coop warm in the winter and cool in the summer. You definitly need to clean it often though to prevent molding. I got some meat birds White rock X and I dont really like having them on hay, it doesnt absorb as much because they are pooping SOOOOOO much. I am in the process of building a seperate meat coop and I think I will have shavings for the meat birds and hay for the hen house.
I put hay in my nest boxes when my Delaware started to lay, and they would eat it all overnight. So I stick to pine shavings everywhere, except the run, where I put big pine bark chips on the areas they have scratched down to dirt.