Sticking out or not, a judo/karate-style belt under an hakama is silly. Period.
A belt doesn't make sense, but pants under a hakama does? I dunno. When I did shindo muso, we wore a blue keikogi, black belt (everyone), and black hakama. No pants. When I did karate, we wore white keikogi, white pants, and belt of whatever color. Now that I do aikido, we wear white keikogi, white pants, white or black belt, and some wear hakama in addition. If you want to judge any of it as "silly", why not judge ALL of it as "silly"? Or why not just leave the judgment aside and get on with it? If the clothing isn't particularly functional, surely the judgmentalism is even less so.