IMHO some governments are thinking about tokenizing fiat especially in Asia because it's a way to make cashless transactions without having to trust a third party like Paypal or WeChat in China.
But it's certainly not for price stability yet as even the big cryptocurrencies are still very (VERY) volatile.
So what now we will have like a GovPay service? Pay through government payment processor? Not that private payment processors can't be abusive, but the government is just horrible.
They will be unresponsive, nasty to customers,after all they have the monopoly on foce... don't like it? Vote for better politicians next time
I'm not sure about the idea behind the mind of the Singaporian government, but I think it's simply to create a token endorsed by their central bank which can act on its value. That obviously doesn't mean that the central bank of Singapore will decide of the value of ETH but only of the value of the token they created.
This token can then be used for interbank or just day to day transactions using the power of the distributed ledger behind the blockchain, knowing that all your token can be changed for singaporian dollars at any time with, I assume, a fixed exchange rate.
So IMO it's basically a way to simplify transaction and to encourage cashless payments.
Another article on this subject here.