Yeah it’s just reflexive ‘do-somethingism’ which falls apart on contact with our actual constitution I think. I’m not saying the Westminster system is perfect, far from it, but there’s legitimate costs to breaking the logic of the system as it exists too badly. It’s not even clear how you would create a written constitution with the same weight most countries have one for example, by definition it’d be an Act of Parliament which any future Parliament can undo.

The Brexit referendum is another great example of why it’s a bad idea, it had the same constitution-breaking property of creating an effectively binding mandate external to the House of Commons which is something that straight up isn’t meant to exist in the Westminster system - it created massive amounts of destabilisation in its own right that the system was never really designed to cope with, without even getting into the consequences of Brexit itself. Compare that to the Scottish independence referendum which was comparatively less destabilising politically, being conducted by the Scottish government under well-defined delegated authority from Westminster it was not constitution-breaking in the same way.