Your first statement seems to imply that the market is flawed (because, obviously, the willingness to pay for something is going to be higher for someone with lots of money than someone with little), the second seems to imply that there is something inherently beneficial in focusing on 'market solutions' as you define them. These views are rather at odds with each other.

But, I'm not trying to comment on either of those, just that you can create utility for a poor person and still have a viable business. If it relies on government for funding, because society has decided it's worth funding that sort of work, so what? We have an entire defense industry in the US based on that idea. Most of our education is too. Other countries have their entire healthcare systems based on that idea. You can decide you don't want to be paid directly by taxed money, but that's on you, not on the viability of such a model.