Community centres are an order of magnitude more expensive than providing tax breaks to churches.
The people are paying one way or another, the question is whether public society will fill the gap or leave it to commercial businesses.
That is one part. However, it is naive to assume people would pay the same for community services.
The other is most of the church work is at heavily discounted rates.
My hourly rate is $160/hr in my day job and I do about 10/hrs a week for my church at $20/hr.
Does your typical government worker ever do such heavily discounted work?