I was then amused to see all the other (Danish) guests arrive within 2 minutes of each other.
You invite 20 people over for a BBQ at 2pm. Here's possible conversations I can envision in America:
"Thanks for the invite! I actually have a haircut appointment at 2, but I'll come right after"
or
"Thanks for the invite, but I have a a haircut appointment at 2..." "what? No worries! Come join whenever you can; we want to see you!" "Great. I will thanks!"
So how would it go in Germany?
"Sorry, I am busy and can't make it"
Because of this, I would say it's even more important to schedule things sufficiently ahead of time. Making up plans only 2 or 3 days in advance, when weekend plans are mostly settled and they can't properly schedule around your event, will just stress people out.
1. the first one can occur, if they can't be on time they will ask if they can arrive later and as the host you get to decide whether they should still come or not, either way the guest will arrive on the pre-determined time
2. if the start time is flexible, this is stated clearly as part of the invitation e.g. you invite people for a bbq "starting around" 2PM (rather than at 2PM) and make it clear that they can arrive and leave at any point in the afternoon, just that they should not arrive before 2PM
The haircut example would just mean you tell your friend in advance that you will arrive later.
I wouldn't say it's an American thing. Any party that's starting at 10PM isn't gonna get a good crowd till 12-1AM in Europe as well. Cause you don't want to show up when there are barely any people and have to awkwardly dance to the music in an empty place.
Party timing is still something many of us struggle with as not every host does it the same. Some like the guests to arrive on time, others have adopted the more international habit of not expecting anybody during the first hour.
Having lived in both countries, I would say our Swiss neighbors are even more stringent regarding punctuality.
Trains are also late in Germany. A lot. I blame DB.
They come up with the silliest excuses too, like that one time were they claimed that the track bed had caught fire. I would have believed it if it wasn't -10°C in the dead winter while it snowed like crazy.
On the other hand I do have a punctuality tick, I have counted out the exact amount of time it takes to get to the train station and I wake up at 0600 with or without alarm clock, regardless of when I fell asleep. I also make sure that my clocks are set as exact as possible (I used to run a GPS powered NTP server just for my devices).
Here in Chicago, the tracks are intentionally lit on fire in the winter (so they don't develop an ice sheet, I think). Maybe the same thing, but whoever explained it was unfamiliar with the practice?
There is also a lot of different snow clearing vehicles that go around in the worst areas.
We do have trainbed fires during dry summers at times (like currently) but not winter, it was just some excuse for lack of trains or otherwise produced delays.
There is a relatively old Swiss movie that plays with them. Available only in French and German versions.
The majority of America just doesn't care about appearance in this way.