Vayne and Yasuo don't have massive weaknesses, they have weaknesses, but they're covered up by other parts of their kit/role.
Vayne has a weak early game, but she'll almost always have a support that will help her stop you from bullying her out of lane. She has no poke, but she does enough damage that she never needs it. She has average range for an ADC, but she has a dash, a knockback, and invisibilty to get out of danger. She's weak to siege, but the threat of her damage can often keep people off the tower.
Yasuo is melee, but he has a shield, a shield that blocks projectiles, and the second best combat mobility in the game to prevent poke. Yasuo needs a knock up to ult, but that knock up can be from any player in the game, including things you can't dodge like a lee sin kick or a vayne condemn. His E sends him at a fixed distance, but he can often use it again before your spell can get there, meaning you need to predict two or even three dodges ahead when trying to land poke against him, and he can often use that time to go a different route.
Vayne is unfun to play against because she has very little counterplay.
She can beat pretty much any other champion in the game in a 1v1 duel when played decently, so unless you have extremely long range and lots of safety, like Cait or Xerath, you can't risk poking her most of the time because she has her passive and a low CD dash that makes her invisible to get to you.
There is not a single ability in her kit that can be dodged aside from the stun on her E, so if she has better stats than you, she wins the fight pretty much every time. This means if she gets ahead, she snowballs hard, and she does percent health true damage, making building against her impossible (No, Frozen Heart and Randuins barely help and it's ludicrous that you'd have to build both every time a vayne is in the game.)
From a non-gameplay standpoint, she attacks in an infuriatingly smug, non-nonchalant way, her model is pretty bad, and her auto attack sound effects are loud and obnoxious.
Yasuo is unfun to play against because (guess) he has very little counterplay.
His Q and E deal instant damage, meaning there's no way to flash out of them, shield yourself, or stun him before he can get it off, you have to predict when he'll use them instead. His W comes out instantly and can block any projectile in the game, with no limits on what it can block or how much it can block.
The third charge of his Q can be dodged, but Yasuo can hold it for ten seconds to pressure, and if he uses E, you can't dodge it. Yasuo's ultimate is instant lockdown extends existing lockdown and deals damage, and dodging it means dodging every form of knock up or back in the game.
From a non-gameplay standpoint, getting killed by an edgy anime guy feels kind of shitty.
Yasuo and Vayne's kit make it easy for them to outplay people, meanwhile, most champions have almost no way to outplay them.
Meanwhile, every ability Lux has is a skillshot. When you trade against Lux, you can come out ahead as long as you're skilled enough to dodge her abilities (Yes, her E and Ult can be dodged.) If Lux has higher stats than you, you can OUTPLAY her and still have a chance. Lux can't farm from under tower forever because she has mana.
If she tries to harass you then she'll push the wave, meaning she can't just sit under her tower, which leaves her vulnerable because she has no mobility. Her lack of mobility also means that if you can dodge her abilities, she has no way to escape from you, so you can kill her without having to keep her locked/poked down 100-0.
ALL of the above paragraph applies to Veigar, except that you can't dodge his ultimate, but it's okay because he's squishy and has no mobility to get near you with its low range. You have to make a mistake and stand in his E first, unlike Vayne and Yasuo, who if they have better numbers than you, can kill you without landing any hard skillshots beforehand.
Having ways to play against other champions is fun because it makes you feel like you're better than them when you beat them, you didn't win because they made a mistake, you won because you made no mistakes, and that feels good.
Winning with skill is more fun than winning with stats, and I'm sure most people can agree with that.
This is earth, and I'm playing League of Legends. Toodles m8.