Look even if she does have the highest level 6 burst damage in the game (which she doesn't for various reasons), I don't care about that. An ADC's job is not to get kills at level 6, and ADC's job is to...carry.
Furthermore, her "burst damage", if you want to call it that, falls off extremely quickly mid to late game. This is because her skills do magic damage, on a physical carry...This makes absolutely no sense. You haven't even factored this into your equation by the way.
Chances are, those AP casters are going to have magic pen runes and the magic pen mastery, which means they'll be doing 20% or more damage with their spells by level 6 than will Tristana, who doesn't use magic pen. More examples of a retarded kit that needs to be updated or reworked.
This kind of inconsistency has been slowly updated over time. From what I remember, Miss Fortune's ultimate used to do magical damage, but obviously that made absolutely no sense, so they changed it to physical. Eventually I'm sure they'll update Tristana as well.
In the bottom lane engagements, her ult is incredibly strong. It is hilariously more versatile than grave's nuke. It is easier to use than ezreal's channeled ult. It is an interrupt. This is kinda important. It can save allies. And, as I mightve mentioned, it contributes to tristana's hilarious level 6 damage.
Her ult in bottom lane, aside from the level 6 burst, which falls off quickly, is good for stopping a potential gank maybe.
Once again, 300/400/500 magic damage on a physical carry is NOT something you want to rely on to secure you a kill, especially considering that it pushes your target away. I can't even count on two hands how many times I've seen Tristana throw away a kill because she misjudged her ultimate and therefore the target survived.
I'd much rather have an Ashe arrow to start a fight, or an Ezreal ultimate which can severely damage an entire team, or secure a fleeing kill, or a Graves ultimate which is actually good as a finisher, and doesn't push your target away. If I want someone to peel for my carry, I'll take a Lulu; I'd rather have an ultimate that does something late game, if it's all the same to you. In fact, I would take Vayne's Condemn over Buster Shot
any day of the week. At least Condemn stuns the target when they hit a wall, and is functionally just as useful for self-peeling as Buster Shot, on a much lower cooldown. It also does physical damage, and scales 1:1 with attack damage, making it much more powerful as the game progresses.
Speaking of team fights, that's really where Tristana fails the most. Ignoring the aforementioned ultimate, which is rather useless compared to the superior AD Carry ults in team fights, she has a serious problem of positioning. It doesn't matter what your range is if you have to stand on the edge of battle doing nothing.
Take for example heroes like Ezreal, Graves, and Vayne. These champions all have really nice positioning abilities, which allows them to kite around in the battle, ignoring the tank, and focusing on the squishier, priority targets first. Graves and Vayne have a dash that comes up every few seconds, and while Ezreal's is a little longer, it's still a great positioning tool, and is what gives him such great mobility in a team fight.
What exactly does Trist do in a team fight? Say the fight has begun and you're standing on the edge of it. Now a Singed runs up to you. What do you? Do you Rocket Jump away? Now you're a million miles from everything that's happening, and your team is left to get slaughtered. Do you Buster Shot him? Okay, you've done absolutely no damage to him and he'll be back on top of you within seconds...While Graves, Vayne, and Ezreal can kite him enough to stay useful in a team fight with their dashes and mobility, he's going to shut Trist down hard. And this is a reoccuring problem for Tristana. She gets shut down easily by zoning. If you use your Rocket Jump to ENTER the fight, you better hope to God that you get a kill or assist before that 10 second cooldown expires, otherwise you're done for.
The only way Tristana can get around this fundamental design flaw is by being SO farmed that even tanks fear you, so someone like Singed, Alistar, or any other tank is going to fear trying to zone you. That's an unreasonable amount of farm to expect on her, which is why she's not used in competitive play.
Also, when I say she can't farm as well as other carries, I don't mean her abilities don't lend themselves to farming (Wow if we're talking purely about abilities, Malzahar should be the best farmer in the game by far...just doesn't seem to work out that way in practice), I mean that other ADCs have a superior laning phase, and superior killing potential much earlier than she does, excluding the gimmicky level 6 magic burst which falls off quickly.
