This would have a lot of problems.
Certain champs, for example,
and many others would be completely useless without any allies, not to mention items like
etc. would become useless as well. If you were going to do this mode, it would have to have certain auras on the map (similar to ARAM) that specifically benefit champs who's kits are based around teams, and the item selection would also have to be tuned as well (similar to Twisted Treeline and ARAM).
Next, assuming you're taking the SR map and just adding bases to the other corners, you'd have a problem with inconsistent paths for all players. Some players would get the river, some wouldn't, and some would have to walk weird paths through the jungle to try and get someone else's lane.
Speaking of which, how would laning work? a four man free for all in laning phase? Sure a free for all would be nice late game, but when you only have 1 skill and you'll die from a few skills yourself, that's just hell for everyone.
Overall, the idea's got some nice aspects to it, but there are so many logistics you'd have to figure out, and the balance would be a nightmare (they can barely balance the base game) for it to actually be implemented.