Doesn't having a character that has the best of both worlds just throw this into chaos?
Being melee completely sucks when you could be ranged instead. There are tons of game mechanics that take a dump on melee characters that ranged ones have an exceptionally easy time evading.
For one - just getting slowed can drop your DPS to 0 as a melee champion, as you'll be to slow to keep up with anything to even hit them. As a ranged champ you can just pewpew-pew in place.
You're also a lot easier to focus in team fight situations if you're in the front rather than the back (melee), and you'll get hit inadvertantly by a lot of AoE bombardments as melee. Also, you have to walk a fair deal to get to a tower and walk away from it, and there's pretty much no chance you can harass someone under a tower without getting shot - where with most mages (1k+ range skillshots) and marksman (550+ auto-attacks), you can smack someone that isn't horizontal with their tower without fear of the tower getting invovled.
Assassins get mage ratios on their abilities and marksman scaling on their auto-attacks so they have something going for them to offset having peanuts for range.