Regulation has nothing to do with capitalism. Capitalists (as in people believing in the free market) are actually opposed to what you're describing. What this non-profit did would happen immediately if there was no government to shut it down because there are high margins and so it's very desirable to enter the market with a lower price - and also charity.
If there was no government to shut down the nonprofit, the company wouldn’t have spent billions to develop the cure in the first place. Why would you do that, if anyone could just copy your work and profit for themselves?
You're very naive if you think that's worth it even in the slightest. See army budgets - and remember that no one will fight for you for your ideas, since you have none. And people (read: other armies) will oppose you.
I cannot imagine charity ponying up $11 billion on anything at all, much less the development of a single drug. Of course, a lot of this cost is due to excessive FDA requirements, but the charities are not funding drug development right now, and I imagine there is better use of charity money, for things that aren’t worth for companies to get into.
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.