It's not so clear to me that a PhD is much use at a start-up in general; you'd probably learn more relevant technical skills at a regular programming job, and

It's not so clear to me that a PhD is much use at a start-up in general; you'd probably learn more relevant technical skills at a regular programming job, and the mental habits you're likely to learn in graduate school will actively hurt you at a start-up. Unless you are lucky or careful about who you work with and on what.