From how I see things this isn't a problem regarding the government's system but a problem with the identity theft happening from the US so I don't think having a blockchain solution can fix all of this when they have created a fraud that can cover something else aside from benefits that they can get from the government. Identity theft can be used in several ways from stolen credit cards to sim swapping and other ways which you can fool any business with a stolen identity. Yeah they can add a blockchain technology in their system but if they want to solve the whole problem then they must focus on identity theft as well.