Methinks it makes Jessie more relatable and interesting that Cloud has no real interest in her romantically, outside of his casual flirting.
Jessie to me was that person who is obviously skilled at what she does, but she doesn't believe she is. In the OG, she actively downplays her work making the mako reactor bomb by saying she just did what the computer told her to.
I'm also being a bit liberal with my extrapolation here, but Jessie strikes me as the kind of person who really mentally punishes herself when she makes even small mistakes.
So when her special ID card she made for Cloud totally shits the bed and sets off the alarms on the train during the second bombing attempt, she absolutely crucifies herself mentally for it. But like a lot of underconfident and anxious people do, she outwardly brushes it off and resolves to fix it next time.
But in her head she's sitting there going "Everything thinks I'm a fucking idiot! How could I be so stupid! And the worst part is it had to be the fucking card I made for the person that I was kinda crushing on a little bit!"
Tl;dr, Jessie to me was that anxious, under confident person who was way too hard on herself. And she's just like everyone else when they're young and have a crush, ain't no fucking way she'd be able to go up to Cloud and ask him on a date, or even flirt back with him to that great a degree.
And that makes her relatable and likeable, to me.
I don't know how much I like her remake persona so far, based on the few trailers I've watched. She seems much more cocksure and flirtatious and, well, #notmyJessie
But again, I've only seen a few clips, and she's a relatively minor character in the grand scheme of things. And all of the above is just my interpretation of things.
Also, it makes way more sense to me that Barret would be more hung up on Jessie, Biggs and Wedge dying than Cloud. If they were going to have anyone lamenting their deaths it should be their leader who pulled them together into the ragtag group of ~terrorists~ fighters that they are.
The cocky soldier wannabe dickhead that is Midgar era Cloud, who hasn't known them that long, being chief mourner? Nahhh.
But again, just an opinion.