I'm not sure I agree that it should be a pharmaceutical company's responsibility to spend their money developing drugs which won't be profitable - after all, it isn't a farmer's responsibility to send food aid to Africa. Sure - if we all put enough pressure on the farmers, they'd agree to send a certain portion of what they grow to an aid programme... but I'm not sure it would be a reasonable thing for us to expect, nor would it be the most effective way for our country to organise food aid.
If we want certain research to be done - and certain drugs to be developed - because we think it's in the social interest, then I think the normal thing to do would be to pay for that through our taxes. That's why we collect taxes - to all chip in to pay for things which we think are in the common good. Obviously, if we want to spend more money on things, we also need to have higher taxes.
It might seem a neat solution to just get the pharma companies to pay for it, but it's a false neatness - there isn't really any reason why it should be done that way, and (like the farmers individually choosing what to send as food aid, and each posting their parcel across) it doesn't seem very effective.
You can tax some industries more than others, if they're more profitable/cause public harm (e.g. tobacco, alcohol etc). And if we honestly think that it's justified and the pharma industry can take it, then surely it would make more sense to be honest about it, and have an industry specific tax - and then pay for publicly-funded research. Then it's clear what society is spending (and what else they could buy for that money) and what we are buying.
Whether increasing the tax rate for pharma companies would actually generate more tax is a separate question, which I don't know the answer to: there's a certain level at which you maximise the tax take from companies. If you tax at 0% you'll get no tax income, and if you tax at 100% you'll get no tax income (because there's no incentive for anyone to do anything) and you get a parabola shape in between. It's the government's job to figure out where the top of that parabola is, in order to get the maximum tax income. I didn't just make that up, btw - some economist came up with a theory about it, but I can't remember his name.