Most homeless are in the big cities, most churches are out in the boonies. The homeless are very unlikely to accept being bussed to a flyover state to sleep in a church in bumfuck nowhere. For a myriad of reasons.
Keep in mind also that a lot of them have a very hard time accepting any help due to past trauma as well.
It's not a situation with a quick fix. Really the first step isn't even ensuring housing for the homeless, it's making sure we don't get more homeless. We likely can't save a subset of today's homeless because they don't want/or won't accept any help that comes with any strings (like no drugs or just they can't trash the place). But we can ensure no-one else ends up on the streets by beefing up mental healthcare and social services.
That's how you get a fancy new prion disease...