Author of FFVII: Lifestream & FFVII: Reflections
You're ignoring the fundamental difference of Jessie being a tertiary character in the original game. She was never going to hold as much importance as Aerith or Tifa in the overall narrative. Aerith and Tifa are main characters, so of course they'd be "everywhere."
The reason why it'd be clumsy and shallow storytelling to include Jessie as a legitimate love interest for Cloud is because of three reasons. The first one being, is that it dilutes and unnecessarily distracts the overall narrative. FFVII, despite it's notorious LT debate, is actually not a love story. Cloud having two potential love interests, one that gets taken from him by his enemy, is enough dramatic, emotional love-story pathos for the game proper. Adding a third just because it's possible literally serves no purpose other than to over-dramatize a factor that was not the crux of the story to begin with. Secondly, it horribly telegraphs the important twist that is to come regarding Aerith.
Cloud having a woman who confesses to seriously liking him die in Part 1 would make Aerith thematically "next on the list." It'd now become a strange, morbid pattern where those who fall for Cloud seemingly end up dead in this Remake. Leaving Tifa as apparently, the survivor of a new bizarre reality game. This isn't a harem anime saga. Cloud doesn't need to be torn between three women who feel for him and want him romantically. It lessens the impact, and cheapens the overall message.
And the third reason is simply, why? It would add essentially nothing meaningful to Jessie's actual story. Considering Jessie is literally living on borrowed time from the perspective of the viewer/player, why would the writers bog down chances to explore Jessie's character independently, with melodramatic, empty attempts at instigating or pursuing a relationship with Cloud? Especially when Jessie would be aware of the fact that Cloud is Tifa's childhood friend? That's time being wasted on an empty, dead-end romance, that could be used to flesh out Jessie's character and make her a secondary character, not a tertiary one. If they padded chances of showcasing Jessie's personality with awkward attempts of her trying to get in Cloud's pants, it'd be worst than just having her remain in the same role as before. They would have squandered chances to give Jessie personality and a character just to create a dead-end, useless and contrived love plot that gives zero pay-off.
So since Aerith dies, is that considered dead-end as well? Why bother having her have feelings for Cloud if she's going to die anyway? That's your argument about Jessie, and it can be applied just as easily to Aerith. Which makes the argument invalid.
Snow and Serah are again main characters in their respective series. So comparing them to Jessie is not applicable either. Cloud doesn't feel "threatened" by anyone's feelings; he's ambivalent at best, or oblivious at worst in the OG. Cloud had other things on his mind. And of course Cloud would react different to the only woman in the group. He's not above appreciating playful flirting. But that's all it is. Playful flirtation. Not every flirt has to be bogged down by the pre-text of a serious relationship or intend to act on said feelings.
... And if you're resentful over the fact Jessie is not part of the LTD, then I can't even imagine the perspective that would create such a feeling. I would think you'd be glad to not have a favorite character bogged down by an undying debate over the imaginary feelings said character may or may not have had reciprocated, that are functionally irrelevant by the end of the game. That's such an unbelievably strange burden to wish to on a character.