I think a big part of the confusion for me is the existence of empty blocks containing no transactions, or consisting only of the coinbase transaction. This means that that the only incentive for including transactions in a block is the fees, which is in addition to the block reward?
Who chooses the selected miners? How do you keep the system from being gamed?
The selected miners are chosen randomly according to their network reputation, determined by network behavior. Meaning the higher the reputation, the more likely they are to be selected.
The system is kept from being gamed by algorithms that freeze addresses engaging in suspicious behavior, for example lots of transactions to addresses outside of the main cluster of the network graph. Similar to NEM's PoI, but without the PoS element. Also transactions are weighted according to whom the transactions are made with, ie. dealing with newb accounts has lower weight.
The problem with these algorithms being that they will freeze innocent people. This could be solved by an auditing process whereby frozen addresses can appeal and be verified by members of the network with a high enough reputation. The verification itself would increase reputation for everyone involved, while fraudulent behavior in the future by the address being audited would lower the reputation of everyone involved in the previous audit.
This is the reason I need to know if having a totally open network is somehow essential to the functionality of the network, like verification speed.
What other purposes does having a high difficulty serve, then, other than just keeping the block time steady?