The general problem with this is that starting a business generally requires money, which for-profit companies get from investors. For a non-profit to do it they need to get it from donors, and then your actual complaint isn't that nobody is willing to start a company that works that way, it's that people (e.g. you and your friends) haven't donated enough money to make it happen.

But something that might be interesting is to start a non-profit whose mission is to create value for customers (i.e. produce non-garbage products), and then all profits go not to a separate charity but to increasing the number of product lines the company produces. Then spin the new product lines off into independent non-profits with the same charter so the organization doesn't become large and bureaucratic or suffer permanent collapse as a result of a single period of poorly chosen upper management.