As a member of the LDS church, the church absolutely does charitable work.

The problem is that it doesn't do $32B worth of charitable work. Or anything close to it. And that, I think, is the problem.

It was meant to be a hyperbole.

Many countries find it useful to encourage some behaviors and discourage others by means of tax policy. Not just the US, although the US seems to do it quite a bit.

So we have, or have had, tax policies in the US that encourage home ownership, marriage, donations to charity, long-term investment, purchasing electric vehicles or electrifying your house, and more. The results of each of these is mixed, and sometimes contentious, but they're all there because congress decided at one point or another that a thing was worth encouraging or discouraging.

(an American) - our tax code encourages behavior society deems virtuous. We "want" people to give money to homeless shelters, outreach programs, overseas disaster relief, etc - so we "push" then to do that by making it relatively less expensive.

I can easily argue that citizenry being directly involved in directing their funds to causes that matter is more democratic than the government doing that on their behalf.