This very much depends on the architecture proposed and what the political drivers are.
A national consumer cryptocurrency intended to substitute cash operations while at the same time offering smart contract functionaltiy would need to solve the same problems that, for example, Ethereum 2.0 is still researching. Namely, scalability (number and frequency of transactions) while maintaining security, with complex on-chain contracts.
A consumer cryptocurrency must rely on a 'large number' of nodes in a peer to peer network to maintain security. If on the other hand the architecture involves a centralised system that guarantees security through central control, a more efficient system would be available through traditional application+database type architectures like Visa for example. A centralised architecture is better achieved through "standard" 'non-crypto'currency. In other words, a central bank that controls M4 money.
Still on the topic of consumer-grade money, it may be that the particular government in question has a problem with local financial entities, money laundering, poor relations with the banks, or some such, so one could speculate that an advantage of introducing any state currency, crypto or not, would be to solve those particular problems.
Further, one possible architecture could involve the 'standard' decentralised p2p network approach, but with state mandates and laws on software client usage. For example, if the developers of the crypto-system could work in tandem with the government on legislation, on arrangements, such as for example "it will become law for users of this system to maintain a node on their computer, but all taxation will be automatic and heavily discounted". This could be a monumental, "epic" achievement of huge benefit both to the cryptosystem and to the state. Cryptosystem developers could work with guarantees of hundreds of thousands of nodes, which would not only help guarantee security but transaction throughput.
Moving away from consumer transactions, the present smart contract cryptosystems suffer from scalability problems. In terms of transaction volume they cannot compete yet with the likes of Visa. If, for example, Ethereum 2.0 delivers on its expectations, the impact will be revolutionary in every sense of the word. Payment infrastructure, settlement infrastructure, and various types of legal and financial institution would likely become obsolete. (It is also conceivable that a state controlled cryptosystem network would be an attractive move for a smaller state trying to shield its own finanical services relevance, for example, from the effects of this upcoming decentralised free-reign global network).
Until then, however, these cryptosystems could only deal with low transaction volume, such as aggregate settlements, land registry transactions and the like. Note, by 'transaction' in crypto terminology when smart contracts are involved, we just mean the signal for a general state transition which could mean anything from an account balance change, to the state of an online contract or video game.
The advantages there are manifold. These include removal of legal infrastructure around land registry. Sales of works of art. Settlement of securities transactions , perhaps of certain types only. Private consensus networks can be established that bond the corporate and state elements of the establishment into a trust-less infrastructure. The fact that adoption is still low is just testament, in my opinion, to the fact that the development groups behind these crypto-systems still can't fully get out of the research and development phases. Projects like Ethereum, Tron, Cardano and so are still either 'unfinished' or in one way or another unable to offer the assurances that you could replace the global financial and legal system with them.
It also occurs to me that in the Marshall Islands it would be interesting to know what the relationship is between Algorand and the govt. If the govt has direct or backhander investment in that firm, this might simply be a way of perfecting a highly scalable proof of stake system that Algorand can take global, with Marshall Islands as the test bed and a stake in future profits.
So in summary, on the whole I think it would be interesting to try and understand what the fundamental political drivers are, and then see what architecture is chosen. For example as I mentioned above, it could simply be that that particulare State is worried about losing control of financial services to some outside entity and wants to take control of the financial services sector. Or it could be that the country wants to appear progressive, and attract young technical talent for some reason. Or they have a direct investment in a commercial development company. Once we have the architecture and the drivers we can list what the actual advantages would be.