What I am particularly curious about is why people tend to believe that NPOs or charities are "especially different" from other businesses. In many cases, there are entrenched non-profits that share many of the same values as their corporate counterparts. There are non-profits and charities that actively support the restriction of access to research and knowledge, almost as strongly as non-practicing entities in court tend to. I exaggerate, but only slightly. Don't even get me started on Komen (the cancer mafia), OCLC (the library mafia), DFA-- any of those.
Watsi certainly offers something unique to the lineup. I remember reading a while back that Science Exchange was trying to get the National Science Foundation to directly sponsor grant money to pay for scientific services "in real time" (as opposed to giving the grant money to the research organizations, which may be better or worse). It would be interesting to see Watsi make up a similar "philanthropic exchange" API where donors can directly cover thousands of campaigns at a time at their convenience and query constraints. Maybe you could next have charities/organizations bid for a contract to solve a campaign problem (like "[offering a cheap but reliable dialysis machine for] dialysis for John"), this way you would be able to incentivize long-term products and solutions as well, instead of just one-time solutions?
I often hear an argument to the effect of "well, charities don't experience a pressure to optimize as much as private ventures do because their incentives are different". But I am not sure how true that is. Some of them seem to be optimizing for convincing philanthropists to make regular, large donations which is a far cry from what you'd think their core mission would be (like "make healthcare cheaper" or "scan and torrent a billion books"). Maybe you can eat their lunch. GiveWell is trying to help this situation a bit.
Non-profits are different in the sense that there are a different set of laws they have to follow, and a core mission that is held to much moreso than in private industry. The laws make non-profits make vastly different decisions than a for-profit would make. Furthermore, non-profits hire people who are passionate about what they work on, which means hiring and culture is different (not based nearly as much on money/payout).
As for a "philanthropic exchange" API, I imagine they are busy just keeping everything running at the moment, let alone trying for something far-sweeping and loosely defined as that.
There are such laws on the books in at least some U.S. jurisdictions, but it doesn't really cause anybody to lose their tax status because there are legal workarounds. It is very common for a nonprofit organization's Articles of Incorporation (and any other legally-binding statements of purpose) to be written like this:
"This benevolent, charitable and eleemosynary institution has been organized [...under the appropriate state law for a charitable organization...] and shall be operated exclusively for charitable, religious, educational, literary, or scientific purposes within the meaning of §501(c)(3) of the U.S. Internal Revenue Code of 1986 as the same may be amended from time to time. Within the foregoing purposes and not by way of limitation, [the organization shall perform its core mission]."