it's not universally bad, it's just important to acknowledge corner cases. It's important to remember that a 'high overhead' though, does correlate to bad performance.
I don't think either of us have real statistics on this. I do know within certain nonprofit (mostly research, but not exculsively) organizations I've been in/worked with, increasing overhead has correlated with my personal dissatisfaction. The place where I volunteer, for example, spent a lot of money on a posh warehouse to prepare food, which was very different from the church that it operated out of - meals then were only delivered MWF instead of daily, and the client base shrunk, there may be a bit of mission creep too (but I'm not quitting volunteering for them quite yet). When I lived in DC, I was dismayed at that location's "parallel" (i.e. does the same thing, but unrelated) organization for similar reasons, except it had gone down the other side and was no longer delivering hot meals even, so I chose a different place to volunteer.
In the sciences, high overhead (as charged on top of grants given by taxpayer-funded organizations such as NIH, NSF, DOE) inevitably means questionably high payouts to the executive-level presidents, and what not. Now that I know how to read 990s, I am looking through the history of a particular nonprofit science research org; 10 years ago it was entirely run off of its endowment and had a promise to the researchers of independence from the tyrrany of grants. Over the course of the decade, the active scientist corpus has shrunk by 3/4, the president gets paid 3x more, the endowment is < 20% of what it used to be, and PIs are being pushed to apply for soft money, and they are negotiating overheads of 60% or more.
Then there are spectacularly bad organizations such as the Harlem Boy's Choir, which I have no personal experience with, but certainly serve as cautionary tales.
