Legendre transforms swap natural variables without creating new physical content. Why do experimentalists construct $F$ and $G$ rather than working directly with $U$?

C. They isolate work limits under lab-controlled state constraints

Legendre transforms alter boundary conditions rather than physical laws; $F$ and $G$ track extractable work under accessible lab constraints ($T,V$ or $T,P$) instead of storing distinct energy. They still retain thermal contributions via $TS$, and entropy remains embedded across their differentials.