That's because you were born when the only conflicts happened under American global hegemony. Shit was never as peaceful as today in the past. NATO states have not been at war with each other since NATO was created - they used to fight all the fucking time, they used to make all the noise.

"Larger armed conflicts". Iraq/Afghanistan don't even come close to being that. Palestine is a tiny microregional conflict. The only reason everything seems big is because everything is louder.

Here is a list of all ongoing armed conflicts, and it is very telling. Painting entire countries is stupid. Russia is included because of a tiny insurgency in the North Caucasus. China is included because of a tiny separatist movement near the Russian border. India is included because of the Kashmir conflict which is just border tension in the North. Anyway that's not the point.

Here is the point:

None of those conflicts are Nation-to-Nation conflicts (Unless you count Isreali-Palestinian conflict and that's complicated). No two UN member states are really in direct conflict with each other - these are the wars that used to be huge, messy, and have been curbed. All of these conflicts (most don't qualify as "wars") are results of local insurgencies. Conflicts involving one or more groups not representing a nation state.

Finally,

there is very little evidence that American intervention helps to prevent larger armed conflicts.

This is oxymoronic. There would obviously be less evidence. All evidence would be of failure. When people do nothing, nothing is happens, and no evidence is recorded. Duh.

We've made huge progress as a world - please do appreciate that.