Atheist - I do think you're oversimplifying the situation.
Yes - religious charities do some good. A lot of good.
Yes - ONE factor that allows religious charities to operate is generous tax treatment.
But - lets look at some downsides:
1) Very few religious charities provide charity at zero cost to the recipient. I don't mean cash cost - I mean 'intangible' costs. For example - if you attend dinner at a Union Gospel Mission, you are subjected to grace before eating, 'helpful' people who will offer you 'counselling' (which is generally linked back to some sort of faith-based position) and innumerable tracts, all based in a faith-based view. So yes - you get a meal. But it ain't free.
Likewise - faith-based NGOs that operate in post-conflict / third world countries often combine their belief systems with the aid they provide. Again - if you have nothing, maybe the last of your concerns is being told to love Jeebus while you're getting your pot of vitamin-fortified cooking oil and 1kg of rice. But it still ain't 'free'.
2) Of all charitable contributions, how much actually goes to the REAL 'aid' being provided, and how much goes to overhead? If I give $100 to the United Way and tell them that I want my contribution to go to say... The Canadian Cancer Society - then the $100 'passes through' the United Way and into the hands of the destination charity. If I give $100 to the United Way without specifying, then it goes into the United Way 'system' - and only a portion (albeit a very high percentile in the case of the United Way) goes to charitable use. If I put a $100 bill on the church collection plate, it could go to pay for the priest's salary, utilities and repairs on the church, expansion of the church, incence, candles, crackers, sweet wine, flowers etc... And maybe $10 will end up going to some church-sponsored mission somewhere in the world - where it will AGAIN be subjected to overhead expenses. Even if I use a church envelope system and specify that my $100 is to be used inthe charitable arm of the church - there still will be significant overhead, and LIMITED fiscal protection to ensure that my $100 ends up providing $100 worth of direct aid. But - your stats assume that the $100 contribution was 'charity'. Well - it wasn't really. It was (most likely) pretty self-serving for the church.
Finally, I think its a little too quick to suggest that a taxation change would end up killing charities. It might change the 'business' of giving, but it won't put 'em out of business. It might also help to encourage more efficiency and more targetted use of aid monies, and discourage the construction of multi-million dollar mega-churches which serve as nothing more than conduits for still more giving (and spending on crystal meth and male hookers in the case of Ted Haggart.)
-AH.