Also since I doubt this is getting dropped and I don't feel like going to bed, on the viability of ADs:
MF hasn't been used basically at all on a pro level since Dreamhack last year, which brings us almost to a full year. Not much to say on her, pretty obvious Riot has needed to do something for a long time. Chaox was trying her briefly several patches ago and TSM used her in some minor events but they wound up dropping her pretty quickly. Don't think anyone would argue she could use a little help, though I don't think she's as bad off as she's made out to be. Still enjoy the character a lot.
Sivir probably got overnerfed in response to her remake making her pretty much god before that IEM TSM won, but she's hardly as competitively ignored as MLG makes her look. The NA/EU metagame favors certain champions and each of the teams have their favorite champions and Sivir is a good example of why that's misleading since she's pretty popular in Korea, ironically mostly to counter Graves, which surprisingly hasn't caught in NA too much yet. She's still has a powerful mechanic with the spell shield that shuts down some lanes and amazing engage/disengage support with her ult and passive.
Vayne could likely use some fine tuning since, like Sivir, she got nerfed from overpowered to perhaps a little too weak to be a general pick choice, but unlike Sivir her unique mechanics don't tend to help her laning so much as her team fight which makes it a little harder to get through the game. However, like Kog'maw she's plenty capable of being effective when comps are built for her, which I'd say is true of probably the middle 3/5 of heroes in the game (with 1/5 on either side being good enough to throw in wherever or bad enough that they don't really belong right now), and there are plenty of decently popular lanes Vayne/Taric and Vayne/Alistar counter. I think one thing that really hurt Vayne was the disappearance of Sona, since she was one of those characters Vayne could catch and eliminate in spite of the whole poke-lane-counters-kill-lane mentality some people had back when there were functional poke lanes bot. Kog'maw is in a similar position as Vayne in being the most severe representation of the AD carries role on the team with the weak early game and devastating late game, but gets better faster(6-7) and has a safer lategame due to his increased range, which makes it tough to pick Vayne over him when teams want a late game AD right now since Vayne is harder to play and offers limited reward compared to Kog if the enemy bot isn't squishy killbait.
The reason both of them see less use now is less due to a lack of power(though that certainly hurts in Vayne's case) so much as how much more aggressive the metagame has gotten at the pro level recently: while it's slowing down slightly, kill counts have been on the rise and game times have been on the decline and a lot of teams like TSM have begun favoring early game champions to try to blow open advantages early, which makes the game tougher for later game champions like Kog'maw and Vayne and obviously prevents them from using that sort of champ much themselves, which slants people's opinions of the metagame since by virtue of winning they were on the stream the most times and played more games than anyone but CLG. It shouldn't be too surprising that CLG is the main user of champions like Kog and Vayne for NA teams, since they tend to favor the longer games. If teams start adjusting their strategy to make it more difficult to blow the game open early, champions like Kog and Vayne would rise in useage without any changes even being made. There's plenty of other champions that have the same sort of rise and fall in usage based on team opinions and strategies in spite of having no change to their power at all: Karthus itself is a pretty good example, since while EU was using him a little more he basically vanished from NA for months outside of some rare appearances with Scarra and now he's suddenly become Regis main again. Cassiopeia did the reverse; she was almost seen as OP just a couple months ago and now she's seeing less use than Kayle(who is basically only played by one person).
Tristana has always been favored mostly be European teams, so I don't think it's a surprise to anyone her usage was so low at this event given that it was almost exclusively made up of NA teams(and of course, almost all of her uses were by Fnatic). Tristana just isn't a character that any of the NA ADs have ever favored much and it's had little to do with game strength because they tended not to favor her even at times when she was considered one of the best options. Tristana doesn't lack favor in NA because she's too weak to use, she just isn't used much because the NA players all have other ADs they'd prefer to master or who fit better into their team's strategies and it's not reasonable for pros to be perfect at every character in their role.
The only one other than Sivir I think actually needs some help is Ezreal, since even though his midgame damage is pretty amazing you have to play twice as well with him to get the same damage as everyone else and he doesn't have massive utility or a really strong lategame to make up for it. Varus might fall under this too; his utility is a lot higher but it's a little disheartening to see how little use he's gotten from the pros since his release... I'd wager Draven will be seeing a lot more use at Dreamhack than Varus will already and that's not a good sign for the character.
The one AD I still think is a big problem is Urgot, just because I find his playstyle to be inherently uninteresting from a spectator perspective (zones more than almost any character in LoL, has a lockon mechanic so the room for counterplay is limited once he hits, swap is kind of exciting but tends to result in easy pickoffs that don't lead to fun teamfights, only really interesting to watch for the camera because of the chance of an enemy getting smeared before they can move which is interesting but not particularly fun), but crowds seem to disagree with me based on the reaction to some of the stuff Urgots do, I guess.
I think if Graves or Corki actually had any balance issues you'd see them drawing bans(which basically or literally never happened) or having higher win rates (see: Sivir at the IEM TSM won, Vayne in I believe Dreamhack last year, Graves at his first tournament), which you don't here; you just see teams picking champions that are reliable and fit the strategies and playstyles they want to use.