Ult does NOT matter in any agent balance unless it's Phoenix. This is because you get them twice, MAYBE thrice in a half. It does not matter whatsoever. Even if it did, Neon ult is still great.
"Higher pick rate doesn't mean she's good" The game aside from few Ranked demon agents are balanced around pick rates.
"her higher sideways speed isn't much" Sideways sprinting is what fundamentally allows Neon movement to be so un-Valorant. If she couldn't jump around and sideways at the same speed she runs and jumps forward, pros will be able to reliably bodyshot the Neon.
"if she doesn't get value early on and wastes her slide and stun, she's pretty much useless" WOW you have not watched VCT in any way shape or form. The stamina bar which recharges is arguably as strong as the slide. I don't care if it recharges slowly, the fact that you have such a powerful ability that recharges passively is broken. It is one of the strongest crosshair breakers in Valorant, not to mention the Neon jump-peeks which every analyst agrees is busted.
Bonus: I'm not calling for a Neon-kill nerf. The devs just need to do something about the sprint-jumps. That's her biggest problem, don't touch the slide, simply rework the way the stamina bar and/or the sprinting mechanic.