List of wars by death toll is very interesting.

There's little evidence for theory that threat of global thermonuclear war creates global peace.

• Even during the world wars, percentage of people who died of violence seems vastly smaller than in typical hunter gatherer societies.
• There were long periods of peace before, most notably 1815-1914 where military technology was essentially equivalent to that of World War I. Before that 18th century was relatively bloodless too.
• One of top ten most deadly wars happened just a few years ago. So even accepting the premise that thermonuclear threat prevents war, we face either wide proliferation, or it won't really do much to stop wars.
• One of the countries with massive nuclear weapons stockpiles suffered total collapse. This might happen again in the future, in near future most likely to Pakistan or North Korea, but in longer term to any country.
• Countries having nuclear weapons engaged in plenty of conventional wars, mostly on smaller scale, and fought each other by proxy.