In my opinion Diana is not broken or weak. Not every champ is meant to be changed.
-Has to wait till 6 to do aother nything (hence why was reworked)
Same can be said to many champions, especially assassins mid-lane that tend to have a high power-spike at lvl6 (fizz, zed, talon...)
-Has no real ultimate
I find her ultimate very strong giving her potentially 2 gap closer that makes her a real treat in a 1v1 matchup. I also fit perfectly with her other abilities.
-Lacks an identity (where should you go as Diana)
I guess that's a personal opinion. I see Diana as a mid, and some people like to use her elsewhere. Same as Poppy, Camille, Trundle that used to have specific role and evolved with the meta and players decisions. Not all champions are devoted to one role only. That also answer your next point which is "can't jungle" as if she was meant to be a jungler. I think she was used jungle the same way Ekko is used/were used jungle. It's not necessarily because they have been designed to be, but because players find it healthy and that evolve with the meta/changes each seasons. If there is a big up for AP jungler for example she might benefit from it. But I don't think (I might be wrong thought) that Riot is trying to make her a good jungle as an individual champion.
To sum it up, she is healthy to me. I don't see her very often, she is never banned, but when I see her, she is not what I would call a weak champion. People playing Diana are most of the time Diana main and they are able to work well with her compared to some more popular champions. I would welcome any main Diana in my team. More than the likes of Yasuo's for example that tend to be way less reliable^^ (but that again is very personal).
And as a conclusion, Id say that with 140 champs if her kit doesn't suit you I'm sure you can find your happiness on a champ that would answer your needs.