He's head of state, not head of government.
That's an arrangement that is useful in different ways to that of eg the US president, and there should be no expectation that the monarch will take political initiatives.
Talking about community spirit and values is exactly the monarch role, and will have been done in consultation with the PM. Especially as he's calling for unity after the riots - deliberate reminder that the authorities now believe they're over.
As monarch, he has a weekly meeting with the PM (the right to be consulted) and the roles the PM thinks may be helpful (visits, lunches, speeches) will be sorted out like that.
What you'll never see is the monarch drawing attention to their role, as they don't need constant publicity for any form of re-election. If you're in a system which means you must either be re-elected or have only a fixed term to make your mark on history, then the quiet and longer-term view probably looks odd/ineffective. And it would be, in that sort of system. But that's not what exists here.