There are two points here, and I'm going to sidestep whether her joining Labour is a good idea and focus on the other.

This government don't need any more humiliation

I'm afraid I'm going to have to disagree with this. We have seen repeatedly that people's memories are like goldfish. You have to keep it up for an extended period to stick, otherwise we will end up with the news cycle burying positive news for boosting the Tories.

All it takes is a bad angle of a bacon sandwich, and the press vultures will completely blow up any negative thing they can to derail Labour.