I think that your ideal picture of the world using blockchain is a bit too rosy. Bitcoin is immutable, Ethereum to some lower degree is, but the type of blockchains you're referring to (if they ever going to be used on a large scale) will be private chains, ones where you do not get to participate in the consensus model they use.
The benefit (for the entities participating in a specific consensus model) is that data can be altered/removed when needed. Immutability is actually an aspect that isn't useful in most industries where decentralization isn't needed. Mistakes are made all the time, which you can't correct with an immutable blockchain.
Fair voting for example isn't going to be more fair with private blockchains of 'independent' organizations. They are highly susceptible to manipulation. For that you would need Bitcoin, a truly independent and immutable blockchain.
Well that makes sense. After all, governments want control over people's transactions. This would be extremely viable with a private Blockchain instead of a public one. While it's no secret that private ledgers are less secure than public ones, they provide many benefits to centralized entities. With a global private blockchain, governments worldwide could enforce their own rules and take the necessary actions with ease. I believe that it'll be quite hard to achieve immutability in a private ledger, as the number of participants are lesser than those in public chains. Not to mention, consensus will be heavily centralized, which makes it easier to revert transactions at will.
The proper model for the New World Order's global currency, would be a DAG instead of a traditional blockchain. DAGs are centralized and perform better than an ordinary blockchain. Governments could this system to their advantage in a similar fashion as a traditional database in order to manipulate transactional activity. The way I see this is that governments will have their own unified currency in the future, while decentralized cryptocurrencies will continue to exist in the mainstream world. Both sides will co-exist given that people will not always use the government's financial system. With a diversity of blockchains, we may be dealing with the Internet of Value within the not-so-distant future.
Nonetheless, by controlling the world's economy with a digital system (either Blockchain, DAGs, or another technology), governments will be able to enforce control over their citizens in a more efficient manner. After all, Blockchain provides the ability to track transactions. Considering that everything is a transaction within the Blockchain (transfer of ownership, identity verifications, notarization, supply chain management, etc) governments could manipulate the world at will. In effect, a New World Order will take place greatly undermining people's privacy as we know it. Just my thoughts