It doesn't always work this way, and very much hasn't in the USA. It's been more akin to:

Fear of invasion creates massive military spending

Massive military spending creates a need for justification, and ability to invade

The need for justification, and ability to invade create wars abroad

Wars abroad create enemies and fear of invasion

Has there ever been a period in history where the dominant military power said "okay, no one can challenge us, let's roll back our military spending" and the peace remained?

I can think of a lot of previous hegemons who got complacent and lost everything.

I can't think of a period in history where most nations were democracies either, where most women could vote, or where most people had access to public education.

But alas, here we are.

And I can't think of a period in history where I can use a tiny device in my pocket to order a coat with same day delivery, but somehow invading Russia in winter still seems like a bad idea.

I see no reason to believe that democracies with women's suffrage and public education are immune to military competition. I certainly wouldn't want to risk massive upheaval of the world order which jeopardizes the existence of all those things to find out.