We are only dealing with a subset of the Bitcoin economy here and whitelisted coins and wallets. Mining is entirely meaningless to this scenario. There is no reason for you to do it.
I'm not sure how mining can be meaningless, mining is Bitcoin.
While you are only dealing with a subset of the economy, I'm processing transactions for the entire network. The reason I do it is the block reward. I'm not going to limit my block reward to whitelisted address transaction fees only.
So, either the government controls mining, or it doesn't. If it doesn't, in the process of seeking a block reward I will be processing transactions for whitelisted addresses and blacklisted addresses, and will be adding those fees to my block reward.
So stop mining if you don't like that you aren't rewarded for it. The government itself can pick up the slack for missing private miners without anyone needing to "control" the process. This is most likely the endgame Satoshi envisioned for Bitcoin in the first place. The rewards of mining will be used by the government in case they need to add new whitelisted coins to the economy, for instance to distribute new wealth to the less fortunate.