In the aftermath of the COVID-19 pandemic, as well as the ensuring culture wars, the American school choice coalition has almost completely unraveled, but many school choice advocates assert that the coalition can be rebuilt. In this essay, I argue that the school choice coalition dissolved not because of politics or circumstance, but because the coalition's libertarians, progressives, and conservatives have fundamentally different first principles in politics and education -- first principles that are present in the works of theorists like Thomas Paine and John Stuart Mill. By studying Paine and Mill, we can understand that any education-reform coalition will be a temporary aberration rather than an enduring alliance.