Wow, you probably want a one-word answer, but I'm gonna give you a paragraph (or maybe 7).
I feel like Lance would be laughing hysterically and nope out of the situation. Keith would probably scream or punch a wall first or at least have a lil broody moment to panic, but yeah after that he'd try to get out of it. Though, is this before or after the lion switches? Are we assuming that this is an au and the lions never happened? Because after the lion switch, Keith could probably be moved to the same category as Lance. But if it's before the lion switch, Lance would be moved to the same one as Keith/Hunk.
Though, yeah, Lance doesn't have enough self-value to believe that he's the chosen one. I think Keith would say no in a more, 'I don't care about your freaking prophecy, let me be broody and emo in peace.' They're both super insecure.
The one with Shiro made me laugh. It is SO spot on. Poor old man just wants a break. I think if this is after the lion switch/Kuron, then maybe Keith would be the one to jump in and be like, 'Nuh uh, stay away from my brother, if he dies again I am gonna be SO PISSED.'
Pidge... yeah. No explanation needed. There's a reason I'm emotionally attached to her/him/them. This angelic demon child must be protected.
Hunk! Poor Hunk. No, leave him out of this, I can see him giving them the biggest, saddest puppy eyes while he says that. He doesn't want to be the chosen one, I feel like the entire team would jump in and try to prevent that. But because he's a perfect angel, he would accept it to help him team and STOP IT THIS MAKING ME SAD.
Sorry bout that. Let's not talk about Hunk anymore.
Allura would see this as an obligation that she has, as a princess and as the (sort of) head of the Voltron coalition. She means those words completely, and will not let anyone down no matter what because this poor bean has too much pressure on her. The whole show was made to portray her as a serious, regal leader. However, she clearly has a dorky side, and her whole role/character would be so much deeper and engaging if this were a bigger part of her personality. 'I will not let you down, and I will be completely serious about it, and you will see the transition from when I was that fun older sister who you can confide in, to the scarred older sister who has seen far too much for one lifetime.'
Can we add Coran in? Because he would be in the same category as Allura, but he would whip out a cape from somewhere and be like, 'Yes! I knew this day would come! I will not let you down!' while twirling his mustache. (Holy crap I just heard his voice in my head crystal clear saying those words. His accent makes it sound so cute!) Coran Coran the Gorgeous Man saves the day! (And he would fulfill the prophecy perfectly, and there would be a giant parade with Coran-balloons and aliens swooning anytime he winks in their direction.)
So, yes. I agree with you.