But how does giving individual families closure benefit the government or society as a whole?
Justice doesn't just need to be done, it also needs to be
seen to have been done.
If you don't acknowledge the need for retribution and satisfying the needs/wants of the victims (within reason), you undermine the legitimacy of the legal system as a whole. People will start to question the effectiveness of the official systems, and turn instead to unofficial systems (e.g. vigilantism) or even not seek any form of justice at all. It isn't restricted to individual families or victims either; the legal system seeks to satisfy the retributive needs of the wider community.
As an example, you can see this operating in any police force. Police legitimacy is a massive concern because once it's undermined, people stop seeking help, cooperating with police and reporting crime.