Why do you think the climate will benefit? Smaller but richer populations have polluted more than large but poor populations in the past. Due to global trade and wealth accumulation, a declining population could easily just lead to more concentrated wealth and more luxury goods consumption (think private jet flights, yacht construction...) which leads to pollution not decreasing.
Similar with war - tons of wars are fought for wealth and resources, which seems unrelated to population, and even with a small population, drone attacks, assassinations and proxy wars are still entirely possible.
You're probably right. My thinking is that with time and with a reduced population the world might become more enlightened. Also if there is an agricultural surplus that it might be put to use feeding the poor. I'm an optimist, and hope the world might one day become an egalitarian matriarchy that learns a thing or two from the past.
Similar with war - tons of wars are fought for wealth and resources, which seems unrelated to population, and even with a small population, drone attacks, assassinations and proxy wars are still entirely possible.