Why would anyone want to own a firm that didn’t earn economic profit in the long run? Is there a compelling reason for wanting to operate a business in this earnings environment? What are the implications for society in terms of efficiency? Are zero economic profits good for society?

This question isn't as difficult as it might first appear. The initial question is essentially asking if there is any reason why a person, firm, or company would operate with zero economic profit. As long as you come up with some kind of viable reason to do this, then you have answered the question. It's conceivably possible that a company owner wants to run his business from a completely altruistic motivation. He wants his company to "make the world a better place." Money that the company earns goes into paying salaries and the necessary things to run the business, and the money could also go into things like charities or organizing community events. Those things won't necessarily give any return on investment. It could help the company image which would then possibly increase income, but the company could then just pump more money back into the community vs. salaries and savings. As for whether or not you think this kind of business model is good for society is up to you. Personally, I think it is. I look at nonprofits like Khan Academy, Planned Parenthood, American Heart Association, and Kiva, and I see a lot of wonderfully positive work happening that is directed at improving people's lives instead of intentionally trying to improve the value of a market share.