Nice idea of OP, but in reality things like team setup is really complicated. since what champions you are going with really depends on what you want to do.
In short, I find that there are a couple of overall gameplay strategies you should have in mind when you select champions.
1) Augmented physical DPS
Basicly this team consist of the Strong physical carries (ashe, ezreal), then 2 champions that augment the damage and protect the carries (taric, janna, sivir, shen), and lastly your wildcard magic dps source to prevent counter by mass armor stacking. (shaco, annie, kassadin, zilian)
This strategy wins by very high sustained DPS, if the enemy is not able to take down your physical champions within seconds of initiation, they will be melted in seconds. and since the carries are protected very well by their own skills (volley and teleport) as well as shen taunt, janna shield, and ulti, kassadin slow, tibbers stun, zilian revive, speed/slow, shaco puppet and taric stun. It is pretty much impossible to win a teamfight against this team unless your enemy brings insane burst damage.
2) AOE nuke
This build use 2 classic Mage DPS style heroes (annie, kassadin, fiddlesticks, zilian). for initiation you need tanks that support the magical damage burst (amumu, malphite, rammus). One physical carry to prevent magic resist stacking (ashe, twitch) one wildcard, that can either be a jungler (shaco), or support (soraka, taric)
The strategy is to force a teamfight, either by pushing or threatening nashor kill. scout well with wards or twitch and initiate once the enemy clump together. Initiate with your tank, and instantly follow up will all AOE skills to decimate the enemy team in seconds.
3) PVE Team
This build want to push all lanes all the time utilizing strong 1v1 champs and avoid teamfighting at all cost. and kite the enemy to death whenever they try to move after you. the natural strong picks for this approach are Shaco and Nidale, the secondary healer can either be Taric or Kayle, for the last 2 spots you can chose a champ like Kassadin, or a strong lane defender and kiters like anivia or ashe depending on what you need. Wildcard champions that are strong for this kind of build is master yi for insane pushing speed, shen for more tankability and mobility, or tryndamare for towerdiving and quick escapes.
The success of this strategy all depends on how well you control the map, and force enemy to split up all the time. Use wards traps from shaco and nidale to get vision of the entire map. and gank enemies whenever they venture a litte too far. while you slowly contain them in the base. If the enemy should try to push out of their base with 5 champions, fall back from that lane immediately, and push the other 2 lanes hard. and some point you will eventually wipe the enemy team at their front door, and you will take down their 3 inhibs in short order.
The strategy here is to set up a base in front of the enemy base, and then slowly take tower after tower. Central heroes for setting up a base the enemy cannot go near are Heimerdinger, blitzcrank and shaco. Besides heimer, you need another hero that can deal damage from afar to soften up the enemy while they are under their tower (ashe, ezreal, sivir). For the wildcard you can pick something your team lack, good choices could be a mage (annie, kassadin) or healer (taric, kayle, nidale).
Building aura items are a top priority for this strategy, where emblem, starks, mana manipulator/soul shroud and aegis should be acquired before hard pushing begins.
If everything fails, you can still easily win the game on the back of 4 man turtling while shaco backdoors everything.
I could write a lot more about how these strategies should be executed, but for now I don't want to spend hours to create a wall of text.