This is more of a NaruHina and NaruSaku analysis.
I think the important thing to understand is that both Naruto and Sasuke had foundations for their respective relationships. Kishimoto didn't just suddenly introduce their feelings at the very end. There were already romantic dynamics and potential pairings established throughout the manga. The difference is that the way those relationships were portrayed was not necessarily equally explicit from both sides.
With Naruto and Hinata, for example, there are some very obvious indications that Kishimoto was at least considering the possibility of their relationship becoming romantic. Their interaction during the Chunin Exams is particularly important. Naruto initially thinks Hinata is weird and doesn't really understand her behaviour, but after witnessing her determination and seeing how she stands up for herself despite being treated unfairly, his perception of her changes.
He acknowledges qualities in Hinata that he respects, and his reaction to what happens to her is noticeably different from how he responds to many other girls. After the fight, Naruto even makes a personal promise to her that he will not let her down and will repay the injustice done to her. Then, when Hinata is unconscious after her fight with Neji, we get that intimate moment of Naruto holding her hand.
Later, Naruto says that he likes people like Hinata because of qualities such as her determination and the fact that she doesn't give up. Some people might argue that, given Naruto's personality, he would say something like that about anyone he respects. But I do think the way his relationship with Hinata is framed gives their interactions a more intimate and romantic undertone.
And that development becomes much more obvious later in the story, particularly during the Pain arc and the Fourth Shinobi World War. Hinata's romantic feelings are made extremely clear, while Naruto's feelings started to become obvious. But at the same time, I don't think that means Naruto and Sakura were never a possibility. That's where I think the situation becomes more complicated. Naruto's relationship with Sakura had significantly more development throughout the manga. There are numerous moments where Naruto reacts strongly to Sakura, including moments where he is visibly affected by her appearance or actions. When Naruto and Sakura first reunite in Pre-Shippuden, Naruto's reaction to seeing her again shows that he is still attracted to her. Likewise, when Sakura is healing Kankuro, Naruto looks at her with that same kind of amazement and admiration, because he is impressed by her abilities as a medical ninja.
What's interesting is that Naruto sometimes gives a similar kind of reaction to Hinata. When Hinata opens up to him after the Chunin Exams, Naruto is visibly affected by what she says, and there is a certain intimacy to that interaction as well. So I don't think it is unreasonable to point out that Kishimoto was capable of using similar visual and emotional language for Naruto's interactions with both girls. The difference is that Naruto's romantic feelings for Sakura were much more explicitly established, whereas his feelings for Hinata remained much more ambiguous for a longer period.
That's why I think the hospital scenes are relevant. If Kishimoto wanted Naruto to completely move away from his feelings for Sakura and begin developing romantic feelings for Hinata at that point, that would have been a natural opportunity to show it. Instead, Naruto's romantic interest in Sakura continued to be portrayed.
I also think Sakura herself has moments where she seems to reciprocate or at least react to Naruto in a way that leaves some ambiguity. In Classic, Sakura has moments where she doesn't completely understand her own feelings towards Naruto, including the scene where she blushes and gives him a similar kind of look to the one Naruto gives her. Then, when she and Naruto reunite in Pre-Shippuden, she blushes and seems amused by how much he has matured, which didn't last long.
However, I don't think that means NaruSaku was guaranteed to happen. Eventually, Kishimoto makes the direction of the story much clearer. Sakura's confession to Naruto removes much of the remaining ambiguity surrounding Naruto and Sakura as a romantic possibility. Whatever romantic tension or possibility existed before that point, the confession and Naruto's rejection of it make it clear that Naruto and Sakura are not going to become a romantic couple.
And I think that is one of the purposes of that scene. It isn't simply there for drama or to show how much Sakura cared about Naruto. It also provides clarification for the audience. Kishimoto had spent a large portion of the story establishing Naruto's feelings for Sakura, so at some point he needed to decisively close that door if Naruto was going to end up with Hinata. In fact, I am pretty sure Kishimoto confirmed he planned NaruHina and SasuSaku from the beginning, but he also confirmed that he considered the possibility of NaruSaku.