If the other employer pays more or works you less you should move anyway, BYOD or not. If the other employer e.g pays less then you’re an idiot to take a 5 figure paycut or work 10 extra hours a week just to avoid buying a $300 phone. BYOD policies are irrelevant in the grand scheme of career planning.

In the grand scheme of things, one should not weight only BYOD policies, but they are certainly a red herring, a sign of employers that don't give a damn.

That’s not what a red herring is, but you are correct that it is a red herring.