Sticking out or not, a judo/karate-style belt under an hakama is silly. Period.
Not necessarily, if you ask my own personal experience. Can be a matter of ergonomic acquaintance!
Without a belt under it, my hakama would just fly away each time my teacher throws me around. The only way to keep my hakama close to me is to tie it's belts around and through my inside belt. Tried all the other ways around and nothing works. Tying the hakama belts alone around my iliac bones creates pain than i cannot withstand.
So it always comes down to very personal somatic and psychic comfort, i reckon.