Philadelphia is home to some of the most venerated medical institutions in the country. Yet when it came time to set up the city’s first and largest coronavirus mass vaccination site, officials turned to the start-up Philly Fighting COVID, a self-described “group of college kids” with minimal health-care experience. Chaos ensued. Seniors were left in tears after finding that appointments they’d made through a bungled sign-up form wouldn’t be honored. The group switched to a for-profit model without publicizing the change and added a privacy policy that would allow it to sell users’ personal data. One volunteer alleged that the...