Both scholars provide valid reasons behind their thesis despite their opinion being in the opposite spectrum. There is no doubt that either view of this problem is without its shortcomings.
From historical experience existence of nuclear weapons changed the rules of the game. According to Walz nuclear weapons induce caution and rationality in any state, discourage pre-emptive and preventive war, and make coercive threats less credible. Sagan's point of view mainly highlights how the decision-making of states, especially in third-world countries is influenced by and self-interests of sub-state actors.
The optimism of proliferation could be understood in the world described by Fukuyama in his book The End of History and the Last Man. If we take into consideration that all countries are democracies the nuclear spread becomes harmless and useless. Why deter other democracies?
In a multipolar world without a "world policeman" where many countries possess nuclear capabilities, international pressures become less effective. States in times of crisis are prone to be selfish and put their needs above international needs. The historic narrative mentioned by both scholars is a little misleading. The idea that it worked back then doesn't mean it will work in the future. The rationality of states isn't guaranteed. Sagan's article suggests that decisions can be influenced by the domestic front and the armed forces. I would like to add additional actors who can highly influence the decision in the future such as corporations and the spread of nationalism, religionism, and radical ideologies.
Waltz advocates that possessions of even a small amount of nuclear arsenal can lead to the reduction of military spending but I view this as an obstacle to the military strategy. The money spent on military research can lead to the adoption of more efficient technologies in the private sector. No article mentions environmental concerns or the burden of maintaining the nuclear program on the state budget. We have no idea what even a limited exchange of nukes between two states in one region can do to the world climate.
I am not keen on the idea of nuclear proliferation but unfortunately, there will be more states acquiring nuclear weapons. I am concerned that in the future if states' accessibility to raw materials and water or fertile soil becomes limited the nuclear states will use nukes against other states as leverage.