By independent, do you mean become solo miner or join peer to peer such as P2Pool (where you need to run full node client)?
I generally meant those who will not work according to the rules of their own or some other government and will process every transaction. Since miners get part of their income from fees, and as the reward per block decreases every 4 years - those who check each transaction and reject them for some reason will certainly be left without part of the income. P2Pool is definitely an interesting idea for those who have the resources for something like that.