Why not take 'unpredictable and swingy' to the logical, unfavorable extreme too then, where everything is rolled including fist circumference?Excellent point. If you take this all the way to its most extreme, you would end up with just one character class, one single species, with the same ability scores and hit points, and the same decision tree at every level-up. All characters would be different in description and flavor only. And you're basically playing Skyrim, on a tabletop. I'd probably still play it, but...meh.
Right now, there's no option for 'actually balanced'. There 'Now', 'the Good ol Days', and 'Comedic Flanderization of Balance'.