And you are telling me wielding an appropriately sized reach weapon as a large creature doesn't give you more reach than as medium?because that'swhat the bracers let you do. Wield like you were large.
Additionallyy, see words "Typically" in above quote. "Typically" you cannot wield a large reach weapon at all as a medium creature.
But then again by the strictest raw, having a natural reach of 25 feet as a medium creature means picking up a 12 foot long halberd suddenly makes your reach 50 feet.