Because it is federated, and no single entity should own and control the data.
> What kind of blockchain will it use?
I am thinking of Hyperledger Iroha. Any other suggestion, most welcome.
> Public or private?
Federated
> What will be the consensus mechanism (PoW or PoS)?
That is the reason why blockchain was choosen.
> My point is, private blockchain doesn't seem to be having any additional advantage at the cost of efficiency and speed of traditional database.
It is not about cost or speed. It is about securing the data in such a way that no single entity controls it. Because the data will be of students, it is better to have multiple trust-worthy entities having an oversight rather than a single entity.