I can't speak for everyone, but my face can feel the difference between a stropped razor and an unstropped razor. I can even feel the difference between a well stropped razor and a poorly stropped razor. I guess if there's an upside to having sensitive skin it's instant feedback

IMO stropping is a daily necessity. If you don't believe me take a razor that hasn't been recently honed or touched up and try shaving without stropping once or twice. You'll be able to tell....