No, you cannot fix the melee vs ranged problem
If you could you need to call the dungeons and dragons guys and tell them they were idiots and you're the god of balance
If you could this problem would have been solved decades ago
The only way to really make everything balanced is to make everything the same, perfect imbalance is the way to go otherwise.
This means that either melee or ranged will be strongest. Trying to balance the two will NOT result in a game you want to be playing.
As it stands ranged champs have an advantage but cannot function on their own which is FUCKING FANTASTIC FOR A TEAM GAME
Then you have games where melee has the advantage where a player is a one man army and everyone else is just the support. Note that supports in this game aren't really supports theyre just budget strategy mages and tanks. Even if you manage the melee is strongest thing you don't solve the problem with your miraculous fix. We will reach a point where there is melee every game
Instead what riot did is gave ranged the advantage and melee the ability to counter in certain respects. It is a reasonable setup and doesn't need major changes. Ranged pokes the shit out of you but if you actually know how to play and get in close its gonna get ugly for the ranged champ. Situational advantage.
show up as they try to get rid of alternative life regen methods.
and 
were not picked **once **at worlds? The boogeymen of mid lane that terrorize standard mids with their extreme potential for skilled players, destroying the lives of solo queuers worldwide. Not picked once, because they can't burst from 700 range like Syndra can. This is what happens when effectiveness is not exchanged for safety, as the only way melees can compete with ranged is being more effective once in melee range.
