Congratulations, you just defined Tanky DPS and the reason it irritates people.
Except I don't think Mundo is that bad compared to the likes of Xin, Irelia, etc.
The other tanky dps characters are mainly assassins that can afford to dive into an enemy team to reach their target. They all have targeted dash attacks with burst damage and stun attached to them, and abilities they can combo immediately afterwards for almost instant death on any non-tank. So they can kill their target and survive the small amount of time that they get focused. They really don't have any weaknesses, other than hard cc and they can't survive extended focus unless seriously fed. There is absolutely no weakness that shuts them down and nobody really stands a chance against them 1v1. If a fed Xin, Irelia, Nasus, Renekton, etc jump out of a bush at you, and you don't have any great escape mechanism, you're really just fucked. There's nothing you can do.
Mundo is the opposite. He has no dash and his only cc is a skill shot. He can survive extended focus and he can dive into an enemy team to cause chaos and drive away carries, but he can't assassinate. He has no burst damage, unless you build him for it and then he's not very tanky. He has definite weaknesses. Ignite effects are very common and shut him down completely if used well. He loses against burst damage early game and high damage/lifesteal dps late game. He generally loses against other tanky dps characters if they catch him in a real duel. If Mundo jumps out of a bush at you, all you have to do is dodge skill shots while running to safety. His role isn't to get kills, it's to draw enemy fire, break up the enemy team's formation, and cover escapes and chases. This is why I say that Mundo is a tank. He's just a different style of tank from your Rammus or Amumu.
Other tanky dps characters piss me off too. They're designed to be super-predators with no weaknesses. I don't understand why Riot keeps making them.