It seems to me that there's a strong Pareto law inclination to this. 99% of non-profits are going to the local volley ball club type organizations that indeed don't make any money at all, or maybe a few hundred at most. I am in the board of a local chess club and you should see the amount of discussion that sometimes happens around a budget of no more than the equivalent of several hundred USD. I honestly can't imagine anyone is using us to launder money. (How, even? Yearly contribution is less than 100 EUR and even major sponsors for tournaments etc are easily traceable local companies that contribute <1k EUR each)

Then there's a relatively tiny amount of organizations that processes the vast majority of funds. Universities, hospitals, big FOSS organizations, etc. Those are the ones that are actually interesting.