Religion (and everything that comes with it) shouldn't be tax exempt. The government should treat the act of spreading "religion" as a hobby rather than a public service. Especially since the beliefs they're peddling cannot be verified by science.
The key here is the word "faith" and it means believing in something powerful enough to create everything we know and all we do not know.
But following you idea, that would mean that sports clubs, drama clubs, art clubs and things like women's clubs, and anything else where there are no profits and nobody take any surplus to their bank. Churches do not distribute profits as they do not have a "profit" so they can not be taxed, just like the Rotary or the amateur hockey team in town.
The scam behind most shifty non profits is how the leadership pays themselves. I'd reckon that the leadership behind some of the larger religious broadcasters are taking home over 6 figures (which is more than what their average "congregation" makes).
And the PBS / NPR CEO in New York makes about a million a year. That's because that person is a "rainmaker" and brings in the corporate and charitable organization donations. Why should a good preacher have to live like Mother Teresa?
And it's not just religious broadcasting. There are a ton of non-profits that are run by people who pay themselves ridiculous salaries while amassing massive expense sheets. Some will even make more money than their private sector counterparts.
And they are paid that much because if they are not, the good ones go somewhere else where there is a board of directors which recognizes that they bring in much, much more than they are paid and are well worth it.
My mother spent nearly 40 years on the board of the County of Cuyahoga hospital system in Ohio, and she taught me a valuable business lesson: thet kept losing good managers to private hospitals, so she helped push the board to raise the pay. They got a good manager, and the systems implanted saved the system many times the salary... doctors stayed on the staff longer.... labs and equipment were improved and more insured patients came because the hospitals got better and they were not just getting the indigent and uninsured.
I think there has to be stronger regulation when it comes to non-profits. Every non profit should have their work scrutinized and their impacts on society measured by our government.
That is tantamount to censorship. The fact is that non-profits are beneficial to society as they do things that for-profit enterprises can't do or won't do. We'd end up without Habitats for Humanity or the Museum of Tolerance and entities that do things of great value for our communities and nation.
We'd be better off fiscalizing the different government agencies to see if they produce anything of value with the money we don't give them voluntarily. The Bridge to Nowhere in Alaska and the Train to Nowhere in California come instantly to mind, but there are hundreds if not thousands of government programs and agencies that exist with the sole purpose of self-perpetuation and which are cesspools of tax dollars doing nothing.