The post I was responding to was arguing that churches don't benefit the community. I understand you aren't though, and you raise a fair point - to wit, churches don't even need to "check a box" (IRS 508(c)(1)(A), pubs. 526 & 557). There are good reasons for registering as a non-profit, though - it enables the contributors to deduct donations from their own income, thus lowering the contributors' tax obligations. This makes it easier to raise money, but is a bit different than the automatic tax exemption that the church itself enjoys. Each exemption warrants its own debate as they're different in aim and rationale. 
I do think it's worth pointing out that most churches do not resemble ABT or ChangePoint, but are small, often sharing facilities with other groups, and have less mature mgmt capabilities than your avg non-profit (that's saying something!). It's hard to imagine many of them filing 990s. Would your proposal's chilling effect on local contributions be a community net gain?