We used to fly 'pure' single role missions with multi-mission crew. Admittedly many of these would turn out as extremely boring for the non-operating section.
OTOH, I can't remember how many sorties had the mission changed either at pre-flight, in the climb, or during the sortie. You would look pretty stupid with a 100% serviceable and capable MMA and the wrong single mission crew on board.
In ASW surface search will become pure acoustic. In ASuW acoustics can gain valuable intelligence.
And that is just a flavour.