He notes the very strong likelihood that there would then be a minority government rather than a coalition of any combination.
And I think he is right too that it would be enormously difficult for a governing party, in a hung parliament situation, to change its leader and the PM. Above anything else, there could well be a major legitimacy problem with the emergence of a new Prime Minister just days after a General Election, when they were not a leader in that election.
So, in practice, I would agree with him that any such scenario is very likely a non-runner. But the barrier is not the one which Kettle gives, of the Labour party rulebook.
He writes that:
Today parties are encumbered with more rules. If Brown goes, Harman automatically becomes Labour leader until a party leadership election is held.
But, with the party still in government (as would clearly, technically, be the case until another PM kissed hands or another government was formed), the Labour leadership rules do not automatically elevate the deputy leader, but rather give the decision about an acting leader to the Cabinet, in consultation with the NEC.
A deputy leader might very often be the leading choice in terms of the politics, but there is nothing automatic about this.
When the party is in government and the party leader is prime minister and the party leader, for whatever reason, becomes permanently unavailable, the cabinet shall, in consultation with the NEC, appoint one of its members to serve as party leader until a ballot under these rules can be carried out.
Read the rules here.