Specifically as to the military: My country's military went from worst-of-history to has-50-helicopters-but-none-that-fly in two big steps: First losing a hot war, then winning a cold one.
Plenty of countries have drastically reduced military spending after the Cold War ended. European police has also mostly avoided US-style militarisation. The UK Police used to hang petty criminals every second Tuesday. Nowadays, they don't even carry guns anymore.