IMHO it would be a better 'double act' if they swapped jobs. Stare-more always looks like he is frightened he might say something that upsets someone. Fine as a lawyer, but not ideal in a politician facing up to a need for serious changes in policies and government actions/decisons that people need to understand.
One thing I like about the deputy is that she makes clear where she comes from and why she really cares. Stare-more tends to make it seem like point-scoring whilst carefully dodging anything you might dislike.
I'm guessing Labour HQ thinks the electorate prefer the current set-up. Starmer is not a natural politician but that can be a plus, and it doesn't prevent him and his team from tackling the major issues e.g. climate. Obviously some - mainly the left - will want him to do more.