The military is so intertwined with US national identity that it's embedded in just about everything from sports to science. The US police forces are the closest to military turned inwards.
Unfortunately the fetish for violence in American culture is baked into the core of American identity and has been since the Second Amendment and the archetype of the armed American revolutionary patriot was seared into the zeitgeist. Americans love Dirty Harry and Jack Bauer and the gritty, no-nonsense cowboy who shoots first and asks questions never.
I mean, just look at our response to 9/11. That should have been an opportunity to reflect on the policies that brought that kind of retribution about, and a chance to reconsider our assumptions about the world and our effect on it. Or at least to bring the world together under a rare common bond of global unity and do something good. Instead our jackass cowboy President said "you're either with us or with the terrorists" and went all Yosemite Sam across Iraq. We'll put a boot in yer ass 'cause it's the American way.
We're insulated as a culture (despite our bragging about our guns and revolutionary spirit, it's mostly bravado) and depressingly immature. It's no wonder our police are the way they are.
For the German situation in regards to sport and the military, see https://de.wikipedia.org/wiki/Sportsoldat (You might need Google Translate or so, if you don't speak German.)
Where on earth did you get that from?
Armed forces are definitely not a big deal, in fact there's hardly any mention of them in public discourse, no parades or events involving the military, you hardly see them except occasionally you'll see soldiers going to their training on weekends on the train since Switzerland has national service.
There's also very little jingoism or mention of historical military activities. Really, hardly at all. And that's a good thing, and as far as I can tell that's how the Swiss like it.