Hot take: Mel is not overpowered.
I agree that she has great range and she can one shot you given the right opportunity, however thats literally half the mages in the game. Her Q costs 110 mana maxed out, forcing you to either always have a blue buff and/or buy a tear item, and even though her Q is almost impossible to dodge, without cc you aren't getting hit by any more than 3-4 pellets from the total 10 at max level. Her W has a base cooldown of 35 seconds at level 1 and 23 seconds at level 5. Even at max level she is extremely vulnerable when her W or E aren't up.
I simply disagree with people that say that she is extremely broken and impossible to play against, when in reality you just have no idea of her weaknesses and how to take advantage of them. She absolutely tickles you until she gets an item, she is extremely vulnerable to ganks due to 35 seconds cooldown on W and she does little to no damage when behind. I will say that if she is ahead she can snowball quite fast, but you shouldnt even let her get ahead in the first place. Even in the late game she cant keep up with pre-fight trading without a tear due to her huge mana costs.
Lastly, her ult. Her ult provides a lot of value to her kit, and I will agree that the cooldown feels a bit too short for it to be punishing when used thoughtlessly. But still, if Mel decides to just burst down one person with her ult, she is left with a lot weaker kit for the rest of the fight.
Overall, I do not think she is broken beyond counterplay. I believe that people need to adjust to her fighting mechanics in order to be able to punish her.