Everyone wants levels and farm, in the sense that they do better with them, but that does not mean everyone needs levels and farm.
XP and gold is limited, there are only so many creeps on the map at any given time. There is also the issue of the enemy team that would rather you not have levels and farm.
The 1-1-3 laning setup has evolved as it is, currently, the best way people have found to allocate available resources, both in the sense of the resources available on the map, and the resources that can be safely taken without the enemy stopping you.
Take for example, a Crystal Maiden. She would very much like to have the farm to Blink into an enemy team with BKB active and then cast her Aghs ult, use Refresher Orb, and do it again while a Heart keeps her alive...
She does not need to, she'll be able to do quite fine walking out from behind a tree, casting her first two spells and watching as a Juggernaut Spins the helpless enemy to death.
An Anti-Mage however, for example, does not want farm, he needs farm. He quickly, as quickly as possible, farms a Battlefury, and then combines it with his high mobility to farm both lane and jungle creeps very fast, builds a strong advantage over the enemy, and then ends the game before they can catch up sufficiently to stop him.
That is not what he wants to do, it is what he needs to do.
Mid has evolved into a 1v1 lane, because being in the middle of the map it has easy access to both runes, jungle, and lanes, it provides all the things strong ganking heroes such as Storm Spirit, or QoP need.
Safelane is usually a trilane, to ensure the team can pick a strong carry, that needs a great deal of farm, and provide them the space to get it, likewise offlane is usually solo, because the general idea of the lane is to pick a hero that though tankiness, elusiveness, or both survive well enough to leech xp and what limited items they need to be effective.
Windrunner, or Mirana for instance can be played offlane, they both have methods of escaping should the enemy attempt to kill them, they can both be effective with limited items, and they can both make good use of xp. Centaur Warrunner is another example, he is difficult to kill both through his bulk and his stun, and with quick levels he becomes rather intimidating due to the high damage of Stomp/Double Edge and the Initiation/Escape of his ultimate. Also while there are many items he would like ranging from Hearts, to Shiva, even with nothing but Boots and a Blink Dagger he can be effective.