Should he? Yes, because clearly they are not a united front, and appear not even to particularly like each other.
Would he? No, because he can't. The Deputy is appointed by the Party, and it would need a vote at the party conference to depose her.
At the moment, each of them is clinging on, embarrassing each other, and ensuring that Labour are going to lurch into the next election with exactly the same issues as they did the last one - a clueless leadership, out of date policies, and an ethos that belongs in the history of sixty years ago.