You're thinking about a whole different world with mentality from this one. Right now the system works like it does - drugs get developed - and so there is no need for charity to do it. Charity is not just taking money and redirecting it, it's also operating a business - yes, you actually can run a business without taking massive margins and being greedy, that's what government tries to do (but fails because of involuntarity and lack of competition).
Don't forget that the charities don't have the 11 billion now because the money goes elsewhere (to pharma corps), but people might give it to the charity if the corps didnt't exist.
The same development could possibly cost less, that's another thing to consider.
Overall my point is that the greed of pharma companies is not because of capitalism because it wouldn't be possible in pure capitalism. It's enabled by the government.