Isnt it kinda logical that if NH dies SS goes down with it?
Yes and no. NH and SS are interconnected in that they both possess half of what it requires to create NS. For NS to occur those two hypothetical relationships need to be deprived of half of what makes them whole. On the other hand, it would not require the other pairing occurring for one of them to become canonized. As an example, Naruto and Hinata could become romantically involved but it wouldn't necessarily have to come as a result of SS. Perhaps the two of them simply decide to come together and form a relationship with each other for reasons beyond Naruto's affections for Sakura becoming null (keep in mind that this is only an example).
One of them could die and the other would still hold the unlikely possibility of coming true. However, for NS to occur they both need to be silenced.
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I mean if Sakura and Sasuke end up together then what does naruto end up with? Nothing. Like Shino (or not if Ino decides to follow up on her I could fall for him comment). The hero cant exactly be the only one without a gf can he?
Naruto doesn't necessarily have to be with anyone. Perhaps Kishi chooses to conclude the manga with no relationships coming to be. It would be interpreted as a means of appeasing all of the fans and a refusal to assume any biased position though. By the way, I don't believe Ino ever made that statement in the manga.