White people didn't leave cities because of the threat of nuclear attacks, they left because there was an incredible amount of racial unrest, violence, and rioting. There is a lot of research on the issue [0].
Climate change is a much larger threat to anyone under 30 than nuclear annihilation is, and the balance of evidence we have says that urban lifestyles (car free/car light, living in a multi family home) has a smaller carbon footprint than traditional suburban living.