Dear bhas,
What you are saying could be true that Kunti wanted to take the blame on herself, but then only if this was a wrong thing, ved vyasa was not just sage, he was revered figure in HP being biological grandfather and also because he partitioned Vedas was considered most knowledgeable figure of the time,if he's said that Mahadev wants Draupadi to marry all the pandavas it becomes gods word spoken from gods incarnation 's mouth so it would become gospel truth. No one would question it as wrong. Even drupad who was unconvinced by yudhi examples agrees as soon as vyasa tells him the boon story
if the stunt was for Draupadi, isn't convincing easy if she is told that 5 husbands is a result of her difficult penance and that too from lord shiva, instead of telling her we r gonna share you coz our mom says so
So logically both reasons don't fit in as apt.
If we don't whitewash pandavas and assume as normal hot blooded males, they had just spent two years as celibates (except bhima). All of them had seen her in swayamvar and all of them were affected by her beauty. ( I won't use lust as it might be too strong and definetly not love because one glance is too weak a reason to fall in love) Yudhishtir naakul and sahadeva left as soon as Arjun won, bhima and Arjun came later so could be that yudhi realizes that maybe Arjun might not be happy sharing, he may still share out of his sense of duty but will always hold a grudge.
So Kunti stunt was to maybe get Arjuna to realize that they have always shared everything, irrespective of who won what and that's what they should do now. And yudhi s statement was kind of emotional blackmail, hey I am fulfilling the responsibility of being th big bro, I give up my right, you have her. Arjun feels oh what the hell my bro is so great, that he can give up the girl for me, then why shouldn't I share her.
Why I am saying this is that similar scenes used to be played in our house over toys, my brother would get toys on his birthday from our relatives like remote control cars but I would get dresses and jewels being a girl, ( typical Indian mentality) and when he would not want to share, I would run to mom and complain , our mom would tell us you should always share and then I would just pretend to be the big sis if my bro still sulked and say with a sad face it's ok if you don't wanna share and go sit in a corner and then my bro will Feel bad and say you can play with too. Always worked, but once my brother grew up he realized what a drama queen I was, and always teased me about it