Fair point, I'm skipping over the need itself. The titular first principle.
First principles: "We need X, how can we accomplish that?"
Higher order: "We need X, what would accomplishing that do for us?"
Yet another incompatible definition - here first principles thinking is define as "how do reach a solution?". If that were true, then it wouldn't be any different from "problem solving".
That's more-or-less the definition, no? First principles thinking and higher order thinking are both methods of problem solving.