Identifying Diana's kit's problems
I'm going to cover this from a couple angles, so please read through the entire thing before argueing.
From stats needed
Cool Downs
At max rank of all of her abilities (with no CDR), she has a 6 second pause after a full rotation. This is an eternity if you didnt 100-0 your target (which is probably why Diana is the only one that can do that anymore). This makes her very feed or fed as she either has the gold to get enough AP to 100-0 or cant secure a kill until the opponent has been worn down. This is exceptionally a problem in the early game.
Mana
Diana has the 2nd smallest mana pool in the game. For a heavily AP champion this is awkward. This is even more confounded when Riot has stated that her shield, the most mana hungry ability she has, is suppose to be used to counter poke while in the laning phase. This makes it so Diana's MUST build mana first thing or get drained while trying to off set poke from ranged champs in the early game. By 6, if a DIana has built mana to survive, she still isn't a threat to the other laner because she has no damage to secure a kill. At this too, a Diana cant roam (in efforts to get assists/kills to bolster gold) because clearing a wave quickly ins't something she can do quickly without expending most of her mana, leaving her unable to help in a gank even if she wanted too. They even buffed her Q to be 55 at all ranks to help.
Ability Power
No doubt Diana's Q is amazing once you have some AP behind it. Due to the prior problems I've brought up though, it is unlikely a Diana has built enough AP to make a difference until very late game. And at that, full AP just makes Diana a suicide bomb as she, unlike most assassin, has no way out of a fight and further dictating mandatory items to even have a chance to survive.
Attack Speed
This is a thing a Diana shouldn't even need yet, to make her passive useful at all, this is required. But I'll go into this further in her kit
From her Kit
Passive
Diana's passive was one of the coolest things when she came out, in fact unless memory fails me she was the second champ to have this (Vayne being the first). Unfortunately, for a caster primary kit, it has little combat application as, unless you built AS, you may get this off once a fight. Quick math, at .864 AS at 18 she can apply her passive once every 2.5 seconds, 5 seconds for twice. But by then your abilities are back up... if you lived that long. It just isn't useful outside of unharrassed wave clear. Even Ekko's 3 hit is easier to proc than this.
Q
Diana's bread and butter, her greatest strength and weakness.
Undoubtedly the uncontested most powerful non-ult/non-triggered ability in the game... which is a problem. You miss her Q, you are out of a fight for 5 seconds at least. You land it, you win. For so much power to be on a basic ability no wonder the CD is so high. On top of that, it has drawn a lot of power from the rest of her kit.
W
Nice mix of damage and defense but is fairly under powered until you get quite a bit of AP, which I explained isn't going to happen till late mid to late game. Also, it's mana cost ramps up dramatically between rank 1 to 5 (40-100, 100 usually being the cost of an ult or use to be the standard at least). Compounding the issue of mana cost in her kit.
E
At the time this was very powerful (and even longer range), but has been nerfed in radius and does no damage. For a non-support that cant fight for 5 seconds after a full rotation, this ability is literally only good for running away during the laning phase (which is ironic because it pulls people to her before slowing them). Mid-late game it is alright to allow allies to catch up on someone you caught, given the rest of their team isnt close enough for them to turn on and kill you. And finally, at 70 mana it is a heavy draw to your pool and only truly good for grouping an enemy team of someone else's ult.
R
Decent range (at release it was ridiculous I'll even admit), but no way out after committing and a decent CD if done without marking them with Q first. This creates a problem in that its damage is so weak in general, has a long CD for that damage, and, as I just said, commits you to any engagement used in. For an ult that is laughably comparable to a basic ability, it really is a weak ult with little use. This is probably due in part to her Q being over loaded. Primarily only useful to apply W damage as, if used right, you have already Q'd them.
I love playing Diana, even still do with a decent win rate (but I do play her HP tank/AP which usually causes the other team to over exert to kill me if they even do), but she is heavily under powered when it comes to champ choices. Specifically, Ekko is a better Diana (I refuse to play him because he has an overloaded kit and think him unbalanced). Though the similar passive, Ekko stacks his much more easily thanks to his Q being able to apply 2 stacks, on top of allow granting a MS boost when triggered. His Q not only having decent range but can hit twice, slows, and, as stated, can stack his passive per hit. His W, like Diana's E, is a mass CC which, though yes is a little more telegraphed, is ranged, slows enemies inside, and if Ekko enters it applies a decent stun and a massive shield, all on top of granting passive extra damage to basic attacks. His E is essentially a flash that can allow him to "flash" again if into a target doing an auto attack, stacking his passive, and applying extra damage on the hit. And then, if that wasn't enough for his kit, his ult heals (increasing with damage taken recently), teleports him to where he was 4 seconds ago, and can nuke anyone in the location he lands.
-Takes a breath-
Diana needs a straight buff or rebalancing, especially when you compare her to Ekko (her closest kit relation in the game besides Riven)