I don't disagree with your math, but I do feel like your assumptions are driven by thought-exercises rather than actual play. Like, sure, this is a good point if every fight starts with both sides within a single-round's move of being in melee, and that does happen a lot. But if its a weird situation or there's terrain considerations (for example, the party is climbing a tower and gets ambushed by monsters from above or the two groups start on opposite sides of a chasm or the monsters can fly or the party is attacked by multiple groups from different directions) then the rogue's range flexibility becomes gigantically more valuable.
The average fight lasts 4 rounds, maybe? If the Barbarian has to spend a single round not attacking for whatever reason, they take a 25% hit to their dps for the fight (and might lose rage, penalizing them further. They'll probably be able to throw a hand-axe at *something*, but it'll still be a substantial hit to their dps). Battlefield flexibility is really hard to quantify, but its a mistake to assume its value is zero.