Well, that's it. My focus wasn't primarily on the tax status or ability to accept donations. I was thinking more about disconnecting from the profit motive and wondering about what sorts of things a non-profit could do that they might not be doing now.
The Raspberry Pi Foundation's experience trying to manufacturer computer hardware as a non-profit is also what I'm thinking of. It seems obvious that some industries would be difficult or impossible for a non-profit to break into.
I will say that my employer has no problems with contacts or NDAs as far as I'm aware, although our legal department can be challenging to work with. Most for-profit vendors can deal with a tax-exempt customer fairly easily. You just have to make sure they get the correct forms.