That's because Vegeta is usually the butt of the joke, the George Costanza, if you will, which again, works for his constantly struggling and put upon character that always gets the short end of the stick despite being the most elite Saiyan ever before he enters the story. Byakuya, on the other hand, is the "winner" in the jokes, deftly negotiating various hairy, ridiculous, silly situations and making others into fools and to look silly, all the while being funny but not acting completely out of character, as he does unexpectedly funny things that would almost seem out of character, but don't, and it works very well.
;D
It's sort of like the "big brother" scene with Seshomaru at the end of the Final Act, or any of the comedic scenes Sesshomaru has with Jaken, really. But as I said, these characters are the higher person in the joke, "the winner,", where Vegeta is the lower person, "the loser." And there's nothing wrong with that. Meanwhile, Byakuya and Sesshomaru both "join in", but don't look silly, remain stoic, as you said. I think the whole gimmick of the comedy with Vegeta is this big, tough, serious angry guy doing all this silly stuff. I'd compare that more to Kenpachi and his dynamic with silly, adorable Yachiru. A little girl that gets to order him around and call him by a pet cute name - "Kenny" or
"Ken-chan", I'll remind you.
Vegeta struggles, he trains, he tries his best. I think it's good to show that sometimes no matter how hard you try, you may never achieve your goal, but you should never give up, because that would be even worse, and people will always respect you for that, regardless of your ultimate win-loss/end goal successes in the end. Saying that Vegeta is ruined as a character because of how he is handled in situations like this or his "win-loss record" would be like saying people should hate Shawn Michaels because he lost so many of his great, memorable matches, and lost a lot of matches in general, therefore he's a humiliated, worthless character and a loser. Not true at all. You can easily lose and come out looking like a rose, and some characters it doesn't hurt at all. Ash loses constantly and it's good because it shows kids that same lesson I just mentioned, plus it's more realistic. You've got to lose a lot to learn things and progress, improve.