Their primary business is not keeping recordings and publishing neatly organized transparency records. Because (a) it's not what the people working for them are interested in, (b) they're heavily volunteer supported, & (c) they don't / can't spend the money to hire someone to do that work.
In the same way someone on Etsy wants to make jewelry, not run a C-corp.
End result... good charities look a lot like bad charities, with limited ability for bystanders to distinguish. In fact, possibly negatively, as actively malicious charities can spend time and money optimizing for externally visible attributes.
The solution is, as you noted, to lean on someone who does have the time to externally audit various charities.
As for charities being run by volunteers The American Red Cross paid its CEO ~700k in 2018 and spent ~110m on administrative expenses with ~89% of their income spent on programs, hardly a loose bunch of people
Just saying and people should make their minds on if the overhead of their favorite charity is appropriate. And they are one of the better ones there are widely known charities with 20/30 % overhead. There was a charity that had most of its income spent on raising money !
https://www.charitynavigator.org/index.cfm?bay=search.summar...
Edit: Cancer survivor charity spends 5% on programs.