IMO it is essential for a couple of reasons:
1. Without a competition to mine, the maximum hash rate of the network is unknown, which means confirmation cannot easily be bounded as adversaries may lie in wait instead of using their power 'for good'
2. With no incentive to behave in favour of the network as a whole, rational behaviour may cause divergence
I tend to think you are correct although I think it could be possible for the reward to be other than "coins".
One possibility that I'm thinking of is service level (e.g. a consensus rule might favour txs from minting accounts over non-minting ones).
This could make sense with the initial P2P application that I am currently working on (being a decentralised BTC/LTC exchange).