Burnham Or Starmer, Still the Labour Party

I am hearing many calls that as Andy Burnham is the new Prime Minister, there should be an election because nobody, apart from the people of Makerfield, voted for him.
The truth is nobody, apart from the people of Holborn and St Pancras, voted for Keir Starmer because we don't vote for people, we vote for the Party and whoever happens to be the leader of the winning Party, by default, also becomes the Prime Minister.
That is why each parties Manifesto's are so important and as long as the new leader sticks to the manifesto, it should be the same trajectory regardless of who's backside is sitting inside number 10.
This is as true as when the Conservative Party went through their role call of Prime Ministers as it is for Labour, the only reason Labour would want to call an election early is if they wanted to change the Manifesto, otherwise it is business as usual only with a different face.
If a Member of Parliament switches sides then i would fully support a by-election because you may have voted for a Party Member who jumped ship to another Party and therefore switches one Manifesto to another which was rejected at the last election but otherwise whether it is Andy Burnham or Keir Starmer at the helm, it is still the Labour Party that the nation voted for who are in power.