That’s a stupid hill to die on. Pick your employer based on important things like comp, work life balance, advancement opportunities, etc. If you have to fork over $300 to buy your own work phone then so be it, buy one and move on with your life.
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.