Because even a dex-based barbarian still needs to hit things, and that means Reckless Attack - because a Barb that isn't reckless isn't really a proper barb ^.^ - and Reckless requires that you use Strength to attack with (even if you're wielding a finesse-capable weapon, and even if your Dex is higher), so you still want a Strength score as high as you can reasonably get it, even if it's not your first (or second) focus. Sometimes you just want to leave the brain and face abilities to other people.
