Wouldn't that still encourage large scale miners to take part? The potential for a reward is the reason all big players are in the game. Just some games offer lower variance rewards than others. GPU mining from what I read isn't incredibly profitable, but there are still people/farms with 150+ GPUs still taking part.

Even if a lottery system was setup, wouldn't it still be worth large farms time to add just enough hashing power to trump other miners in an attempt to try and increase their chances of winning? And doesn't someone still have to control the lottery system that is used to reward miners? Maybe it's my lack of brain cells, but I don't see anything short of a centralized system that would provide incentives for small miners while discouraging large mining farms without some sort of human control.

And to your point, if people spend $50B a year on lotteries, why wouldn't a large scale miner spend the same said money on said lottery system?

Not trying to knock anything at all, I'm just trying to figure out what incentives a miner would have to mine/secure a network and not receive some sort of profit for it? The only way I see this working is the issuing authority and the mining/securing are all done under the same rough, or umbrella but spread out over the globe.