Without a profit motive, how would people decide what they should work on? Why should they work on curing cancer rather than making a machine that counts blades of grass?
I'm surprised this hasn't been brought up before given how many times it has been suggested. I'm with Sakura though, I'm doubtful as to whether or not it'd add much beyond confusing micro leaders but I'm not totally against the option.
I've lost count as to how many times people have attempted to form such a thing. To your credit though, I don't recall any of them writing so much for it.