The game is balanced for high elo, as it should be.
The reason Master Yi dominates low elo is because he has a low skill ceiling. This means that you don't have to be amazing at the game to play Master Yi to a standard that is higher than Bronze.
One thing you need to do is look at his kit. So his Q is his only gap closer, his W is a heal, his E is an auto attack buff and his R gives him attack speed, movement speed and slow immunity. This means that his main method of outputting damage is with basic attacks.
Given this information, good items to get against Master Yi are often
and
as they massively reduce his damage. Good supports to play into him are:
and
as they can both cc him and build the items above. Alistar especially as Alistar can W Yi away from carries. This is called "Peeling" when you peel away danger from your adc/mid.
When playing against Teemo as support you should always get the sweeping lens trinket so you can find and clear Teemo shrooms. Also realise that the shrooms are his ultimate ability. When compared to other top lane ultimates like Trundle's it's really not that strong, especially when they can be cleared so easily.
Veigar has no mobility and his trap has a high cooldown. All the other mid laner has to do is let veigar push and bait the trap when their jungler is nearby and Veigar blows flash or dies.
Nasus can't trade in lane against a lot of top lane champions until he has a reasonable amount of stacks, a good top would deny Nasus the lane entirely by only last hitting waves, making him useless as he'll always be understacked.
Certainly in Bronze not many people know how to play against Veigar/Nasus. I climbed out of Bronze playing Nasus. You let the enemy laner shove you under tower and stack under tower as best you can and then splitpush, TP for a drake/baron fight, 2 shot the enemy ADC and win. You can do that in low elo because supports don't peel or even CC lock you.
Which supports do you play?