"None of which detracts at all from the fact that people can move to find work - they do it all the time".

A subtle distinction, perhaps, but an important one. I know lots of people who have found a job elsewhere and then moved to it - I have done so myself many times. I know a handful of people who moved to London without a job in the hope of finding one. None of them managed it, though one had seven zero hour contracts simultaneously in the hope of making enough to live. Didn't work out.