I feel that Morde is another good example of a balanced Melee DPS. He's a lot like Jax in that, his spells are all really effective by them selfs, which means you can unload your abilities and finish guys off with some auto attacks. This kind of play style sounds more like a nuker, but because of how these characters scale mid to late game, it allows you to build for DPS items while still having that mild nuke capability.
Characters like Yi and Trind are much more item dependent late game, and tend to be easy to keep away from creeps early game. This isn't the case with Morde or Jax, which is probably why they are viewed as much more successful Melee DPS heroes. Jax can harass early with Leap Strike and is a threat while being attacked by the other teams creeps thanks to his dodge and stun. Morde can just sit at range and build up shield to allow him time to wade in and get the last hits he needs, all while keeping his opponents behind there creeps, afraid of the damage he does early game.
It really is a different play style. You can't run in head first and expect to come out on top. In most cases I play clean up as a Melee DPS. I'll hide until I find some one week to pray on, and getting that kill can brake up the communication of the other team, leaving them disorganized enough to make mistakes in my favor.