Blockchain ensures transparency, so you have to ask yourself of governments are interest in more transparent public systems, and what would be the advantages for them in adopting Blockchain technology on these matters.

Personally, I don't see great points for governments to implement Blockchain on administrative, educational, health,  areas, because the such data is considered confidential in most cases. Moreover, it would leave trails, in case members of the government tried to fabric or manipulate data at some point, what isn't interesting for them.

Their only interest in Blockchain is to track citizens funds movements in real time, so they make sure to raise the income through taxes for the public vaults.