Being 86,I cannot rmember (in peacetime) any member of a government who was not a member of the party that was in power..
However,having said that,during WW2 the government was a coalition made up of members of the main parties.
So,I don't think there is any legal reason why it couldn't be as you wish,it's just not been done.
Mind you lots of things that are just tradition need changing,so maybe your suggestion could start the ball rolling?
Good Question Mrs.Sippy.