As I understand it, the term "tryhard champion" refers to a champion who can run in and smack you to death without having to think about it or already be majorly fed. Tryhards do this in one of two ways. Either by being so tanky that they can turret dive you, kill you, and then walk out without having to setup a dive first (Tryndamere), or by doing so much damage and being so agile that they can just blink in, kill you, and blink out without having to worry about counterplay (Yasuo, Katarina before rework). Teemo was designed to counter the tank variety of tryhard.
Teemo's Blinding Dart is meant to shut down a tank's ability to hit you while turret diving, his poison lets him whittle away tanks from a distance, and his mushrooms are designed to force players to actually think about where they walk. Having said that, Teemo was designed before gap closers became more of a thing, and has less purpose in a meta where AD carries can go top and kite tanks better than he. Teemo is currently below average (hence Riot's buff to him last year), and in my opinion his Move Quick holds the biggest need for change.
I know this won't be a popular sentiment, but I have little respect for people who complain about Teemo. There are several ways to counter him, his mushrooms alone have at least three different methods that even a support can use, and he is both immobile and squishy.
But Teemo can go invisible!
Rengar, Twitch, Evelynn, Akali, Kha'Zix, Shaco, Talon, Vayne, Wukong
But Teemo doesn't help in team fights!
Fight in the nest of mushrooms he set up for you 30 seconds ago just as you would fight next to Heimerdinger's turrets, Zyra's plants, or Illaoi's tentacles. Also, see Split Pushing.
Whenever I see a character or class in any game where people simultaneously complain about the playstyle being overpowered while also calling it weak and worthless, I know something's up. And almost always that's because it's a playstyle with its own unique advantages and disadvantages that doesn't always run parallel with the established meta. If you want to nerf an overpowered champion, Yasuo, Zed, Camille, Vayne, Quinn, and Tryndamere have been patiently waiting. Don't complain about the guy who's ultimate requires him to anticipate the enemy's future steps.