So let's say Edward VIII gives up Wallis Simpson. With her out of the picture, there's no abdication crisis and probably no George VI.
Do you think it would have done anything to shake up British politics post-1936? Even during his brief reign, he refused to impose sanctions on Italy after it invaded Ethiopia. How do you think he would have reacted to appeasement or to the start of WW2? Granted, the monarch is constitutionally bound to support the prime minister. But Edward was rumored to be sympathetic to fascists. If so, do you think his sympathies may have changed his stance during the war or his ability to motivate the British public?