> If center-left folks flipped on immigration, the current right wing populism would collapse,

This theory is false, it does not work. It was tested to destruction in the UK this year and tl;dr: it's how to annoy everyone. When the centre-left party chases the right-wing, they disillusion their base and lose votes there, without gaining any significant number or right-wingers, who still prefer what they see as the "real thing". And the right-wingers are emboldened, not collapsed - they take one step back for every step taken towards them.

The long version is here: https://osf.io/preprints/socarxiv/zbmp3_v2