Here is what the article mentions as the positive benefits from using blockchain:
"This story shows and demonstrates the true potential of blockchain technology. The powers it can lend to any system with easy, fast implementation and low cost are irreplaceable. There are many different aspects of public services where blockchain can bring about a revolution. No more standing in long queues and waiting for your turn while filling out and printing dozens of forms. It can all happen with a few clicks."
Quick, secure, cheap, user-friendly.
For example, instead of when opening a bank account in the UK you don't have to go in to the bank to schedule an appointment to go there back on another day to actually fill in the application, instead, you could apply for your bank account digitally and provide your information that way. And only after that they have fixed this issue and taken the step towards being digitally present, we can start discussing about implementing blockchain for these services.