If profit is not necessary, could you give me one reason why anyone would fund a startup? Could you explain how to build a factory if the bank won't give you a loan? How to expand internationally once you've invested all your personal wealth into your business? Why would someone risk being a business owner and not an employee?
See, all these are things that are typically solved by equity investment, or (partly) giving up your ownership, and these investors, for the large risk they are taking, expect a return - profit. Interestingly, as an example, in Islamic finance it is okay to turn profit but it's forbidden to give loans and ask for interest which is understood as making money without taking a risk.
Or, in other words - the business generates value for customers (otherwise they would not buy its products), for employees (who get wages), for loan providers (because you pay interest on your loans) and finally for owners who are running the largest risk - a risk that there won't be anything left to pay for their investment in the company. You would suggest to let them take losses but not have the option of getting profits... and I think it would not work :)