I like playing AD but hate picking a champion/How do I stop playing Vayne?

My mindset when playing AD is that I want to carry the team to victory from start to finish. More often than not I play AD after a few games where I'm mid or something and our MF rushed BT, mercs, and LW, and does no damage. But anyway, based on my playstyle I will always rush IE or PD, as crit is the best scaling stat in the game.

My problem is the pool of AD carries in the game. The 2 things I need to have fun and execute my playstyle are 1) Damage and 2) Mobility. This is how I think of each carry. Keep in mind this is purely my opinion and is based entirely on how I like playing; imagine "imo" and or "based on my playstyle" being in between every word because I basically had to go back and edit out 500 of them.

Ashe: Almost outclassed by Varus but her frost arrows give her much more consistent CC. Using her 1st crit at level 1 and hitting W can almost guarantee a kill with a competent support. This tactic can be repeated to some effect every time you return from base. Overall I prefer Varus because 1) I don't like attempting cross-map ults w/Ashe, so I disregard the range advantage of her ult, making his superior as it cc's multiple targets and 2) He has infinitely more steroids than her.

Corki: 10% true dmg/hit is good but overrated; that's only an extra 100 damage per 1000 you dish out. His Q isn't worth the mana early game and isn't worth interrupting your stream of crits to use for damage late game. His W is an Ezreal E with a travel time and typically less damage unless you're being chased. His E can do a lot of damage, but you have to be constantly attacking while using it to be effective and thus limit your positioning abilities and make yourself predictable. I basically consider this skill Corki's steroid, as it shreds armor and does high dps, but it's hard to know how much actual damage it adds to his kit compared to other steroids like Kog's and Vayne's, so I assume it's a considerably smaller number. His ult only feels useful early game and burns mana, but it's fun to use. It's also good for cs'ing.

Tristana: I loved her for a while because I used to value having a range advantage more than I do now. Her Q is a bit underrated; I do max it out first and I do use it for extended trading in laning phase. Her W is among the best of the AD carry mobility skills, especially b/c it resets on cd, her E is too gimmicky to be useful until lategame for pushing or for really advanced heal-tampering early, and I avoid leveling it early because it pushes the lane. I treat her ult like a second escape, which combined with her W makes her a good solo queue choice (teams generally can't protect the ad in solo). The damage is almost negligible.

Caitlyn: Probably my least favorite champion, all she brings to the table is an annoying but effective range advantage that might get you a few uncontested trades early game, and a good poke. I find her net useless and her ult feels like a basic skill with a lot of range. Of course it does a lot of damage if she's fed, but the fact that it can be blocked and leaves you locked in place (the epitome of non-mobility) makes it infinitely less useful lategame. Her traps are just plain anti-fun.

Sivir: Her Q hurts a lot and spell shields are obviously useful, but her steroids don't give her enough damage for me to want to play her. Of course she has mobility out the ass, but she takes a lot of micro for her damage to meet that of other carries. It doesn't help that I really don't value pushing as a mechanic and her kit pushes like crazy.

Ezreal: I used to main him until I understood steroids better. A 50% attack steroid that you only get for landing 5 skill shots isn't very appealing to me. His Q is only useful early game and eats a lot of mana. His W makes him a fearsome duelist when facing another AD, but it's range is a bit short for it to be practical in teamfights, it eats mana, and casting it takes time away from auto attacking. Lategame, in order to use him to his full potential (ie activating his steroids) I have to consistently land skillshots that have long since fallen off and use up time I could be critting, and if I lose the opportunity to keep landing skill shots his steroid goes away and I have to start it over again. His E is obviously an amazing mobility tool and an early game burst tool. His ult is fun and effective but can be dodged or negated a lot easier than you'd expect, especially given it's chargeup animation. Overall I enjoy him as a champion and he's the AD I think of when I think of mobility, but his kit lacks the consistent damage I like playing with.

Graves: He's a beast in laning phase thanks to his high burst Q/R, repositioning steroid, annoying as hell smokescreen, and defensive passive, but lategame his Q/R falls off a bit and his steroid isn't as good as some others. Overall he's one of the best AD carries but I often pick Vayne over him because her steroids are better and her mobility is on a lower cooldown, which I usually prefer to burst damage.

Varus: His passive aspd steroid is incredibly helpful for csing but is too short of a duration to help trade in the laning phase. Later on it can snowball teamfights massively. His Q does outrageous damage if you charge it and don't hit minions first. His W is pretty good but feels flawed in design; to activate it I have several sub-optimal choices: 1) Use my Q uncharged and waste it's damage potential, 2) Charge up my Q, killing a lot of momentum and making me vulnerable, 3) Use my E, which is sub-optimal because it's essentially his only escape, so putting it on cooldown to proc his W can leave you very vulnerable. Altogether this makes his W an average steroid outside of laning phase and situations where you could probably get away without it anyway, but very powerful if used correctly when laning. As stated before, his ult is a short range multi-target ashe ult; it kicks ass. Overall he lacks the mobility to make playing him very fun for me until I have at least a PD and his steroids are hard to make use of, so I again often pick Vayne over him.

Kog'Maw: His Q gives him a crapton of damage, his W gives him a CRAPTON of damage and range, and his E gives him a little much needed cc. His ult is basically in the same boat as Corki's; it doesn't fit my playstyle very much and lategame I see little reason to use it. Overall he does the most damage out of the AD pool which make me really want to pick him, up until I concede that he is the least mobile and just pick Vayne again.

Miss Fortune: Her passive speaks to my mobility loving but is too easily cancelable, her steroid is decent but doesn't last nearly long enough, her E is pretty much garbage, and her ult is extremely situational. Supposedly her Q makes her the best early game laner/trader of the ADs but I find the bounce unreliable and the skill in general just boring to use. Overall, once her passive is canceled she brings almost nothing to the table that someone else doesn't do better.

Draven: I haven't played him yet. In theory he does around as much damage as Kog while having a great mobility steroid and great damage+range on his ultimate along with some cc on his E, but his damage output is very difficult to optimize in teamfights due to having to catch blades while meeting your normal positioning needs. Since teamfights are arguably the most important part of a match, I'm not sure what to make of him. He can definitely kick my ass in laning phase due to pure damage output the same way Kog can.

What this all boils down to is that I always pick Vayne because she offers the right mix of damage and mobility to meet my playstyle. Because of this, she's getting old, which is making me play AD less.

What sort of things do you think I'm missing or am wrong about? I'm actually anxious for someone to convince me that another champion might meet my playstyle better, or to at least help me value some of the champions I don't like as much. Thanks a bunch for reading.