Diana relies heavily on getting ahead in order to be effective. If she gets behind, she'll have a very hard time getting back into the game. I'm not saying that this is a healthy mechanic, but do know that if you nerf her anymore, she's going to be completely useless. Not to mention, in midlane, she gets shit on by practically any caster pre-6. Diana has practically no carry potential even when ahead. She's snowbally, but her main damage output comes in her double R, which is single target and her ult. She can deal a shitload of damage, but she doesn't have the tools to carry a game like a fed Riven or a Kat can unless she's really stupidly ahead. (Not saying she can't carry through smart plays and such though. Diana just doesn't have the ability to rolfstomp even when ahead.)
Diana probably has the highest single target insta-burst, but that's extremely reliant of hitting her Q, which is a slow moving skillshot that costs her a lot of mana. Diana's mana issues are terrible. The best way to counter a Diana is to engage onto her while her Q is down. If she misses a Q, punish her for that. She has no escapes and with any tank that has hard CC, you can kill her pretty easily even with her double shield. If she tries to kill someone, she won't have the double R. Counterplay to Diana is simply staying out of her range until she blows her combo on a less optimal champion. Unless Diana is stupidly fed, she cannot insta-burst a tank.
I don't think Diana is balanced. Diana's issue is that she doesn't really belong anywhere. She's not the best toplaner, is 6 reliant for ganks in jungle, and gets shit on by a lot of champs on mid pre-6 (plus if she gets camped mid, she becomes useless for the rest of the game). Diana has always worked best as a counter-pick. In fact, I would actually think that Diana is currently underpowered because Riot can't decide if she should be a bruiser or an assassin, so she's a little bit of both and it puts her in an awkward position. She can single target burst, but she has no escape. Her optimal burst combo actually takes way too long to pull off for an assassin, but why build bruiser when you have the capabilities to one-shot a squishy? In teamfights her job is to literally kill the squishy and then hope to walk out alive. I don't think she needs more burst, don't get me wrong here, but more so a defined identity. Where should this champion go, and what should she be good at? Brusier? Better base values lower scalings. Assassin? Lower base values, higher scalings.
According to Champion.gg, her pick rate is 11% (mid and jg combined)h. Her win rate is just around 50% mid and 52% jungle. That's not all that high. Hell, Lux has a higher winrate. On probuilds, you can see that she's picked 0.4% of the time by pros and the same winrates. If Riot could move the power around in her kit so that she has more of a defined role it would solve a lot of the issues people have with her.
Just my 2 cents.