“I don't know if I can ever let Papyrus into the Royal Guard.”
So, I’ve always seen Undyne’s unwillingness to allow Papyrus into the Royal Guard a bit differently than I think the usual consensuses are. While it seems to be taken as a way of showing Papyrus is cinnamon roll too precious too pure innocent bean so oblivious protect him, I always felt like it was more... the opposite?
I could (and almost did, a few times) go into a larger rant about this, but I think if you play UT without knowing anything about it, vs knowing a little about it, Undyne and Papyrus are both meant to be seen a bit negatively until various turning points. Papyrus is probably meant to be seen as stupid and inept and weak, all things that he is not, and through his fight, his date, his friendship and calls, and eventually Undyne’s confession, the fact that he is not all of that is revealed. He’s not in the Royal Guard because he’s too nice. Not because he’s weak. Not because he’s stupid. Not because he’s inept.
(but if you go in already knowing Papyrus is (and monsters as a whole are) nice/sweet/cinnamon roll, I think it has the opposite effect of making him seem weak because he is nice. I don’t think that’s the message at all the scene is meant to convey.)
That moment is supposed to be a final affirmation of who Papyrus is as a character, a nice guy who isn’t the right fit for his dreams because of his morals and good character, not because of his (supposed lack of) abilities. This moment is also the start of softening and revealing Undyne’s character, showing the level of care and concern she has for the people around her, which, to this point on a pacifist run, you likely would not have seen.
So basically, what I’m saying is, I don’t think this was meant to be a sign that Pap needs to be coddled and infantilized, but a sign that he doesn’t need to be. He’s tough, he’s competent, but he’s just not a solider.
But there’s more to it than just that...
While Undyne cites the fear that Papyrus would just let himself be killed as a motive for why she doesn’t want to let someone so nice into the Guard, I feel like this was also an early hint at the nature of LOVE. LOVE changes souls and causes them to harden and change, and it’s effects on a human are strong enough to be noticable, but it seems likely that monsters, who are more in-tune with their souls, would react even more to gaining LV. Wanting to protect Papyrus and his innocence and niceness likely goes beyond just a worry that he would allow himself to be killed if placed in that position.
Because if it’s kill or be killed, and Papyrus did kill (because Undyne trained him seriously as a solider, instead of just cooking lessons and roughhousing), he would gain LV and probably lose the part of his personality that Undyne admires. That nice, innocent, friendly part of Papyrus’s soul, would be chipped away, and Undyne perceives that that would be her fault for placing him in that position.
So I think it’s a lot more than just Papyrus being seen as too stupid to protect himself. I think Undyne’s considered both options, but the other doesn’t come up because you aren’t meant to know the nature of LOVE at this point, and because she’s not going to go into the minutia of her hard-thought decision to an eight year old.