I think the disparity between German & American driving accidents/drunk driving rates is due to several factors...
1. As mentioned, driven mileage per year is a significant factor. Deutschland is a seriously urban/suburban environment, populated by ~80 million, and only about 1/28th the size of the USA. 'Bout the same size as Colorado and Maine combined. You can drive to anywhere in that country and arrive before sundown, unless there's a Stau (massive Autobahn traffic jam). Not that many people do, because...
2. They have a terrific (reliable, fast, affordable) rapid transit rail/bus system that goes to almost all locations (including rural areas). People use it instead of driving for a lot of daily commutes or for trips to distant locations.
3. Gasoline/diesel is frightfully expensive (by American standards). Up to $5.80 a gallon as of Fall 2019. That cuts down on actual annual mileage for most. Driving is an expensive privilege.
4. German kids benefit from a looser tolerance of alcohol at a much younger age (both legally & culturally). By the time most teens start to hit the club circuit, they've been able to drink at home (family meals, outings, festivals, etc.) for years. Many years. There's no great mystery attached to alcohol as a "forbidden fruit". Honestly, they're just better social drinkers than peer group Americans at that age. Less over-indulgence and more previously tested ability to handle it. German kids learn to drink first... then to drive. The opposite of what we do with our kids.
5. Young Germans pay through the nose for expensive (and legally required) Driver's Ed training. Easily $2000 spent before being allowed to obtain a license. That training makes a mockery of most courses in other countries. Among other things, they are required to competently handle Autobahn speeds, superbly handling cars, and a culture disdain for incompetent drivers. Germans regard Driving the way many Americans regard the 2A. As a creator-given Right. They're simply better trained drivers than young Americans. And a sure way to lose that freedom of the road... is to have an alcohol incident while driving. Courts are not very lenient. DUI penalties are pretty severe.
6. Mechanical inspection standards for vehicles are much higher in Germany than in the USA. No rusted out or mechanically unsound Hoopties allowed. You either keep your vehicle in annual inspect-able Autobahn-worthy condition... or you ride the train. People have to spend a lot on their vehicle maintenance, a lot on fuel, and a lot on insurance. They tend to guard their investment by driving competently. Faster than Americans, but generally more competently.
The ironic thing is that all-out Autobahn speeds are mostly a myth these days. The place is so congested with traffic, that speed limits abound. So do traffic jams stretching to the horizon. There are still a few locations where you can wind it out, but fast moving traffic around many big German urban enclaves is about what you'd encounter anywhere else in the world. Just a bit faster on average. Say 90-100 mph instead of 70-80 mph. Or simply bumper-to-bumper at a crawl.
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When WWII American hero 1LT Audie Murphy first returned to US shores, he was denied a drink at a bar because he was still under-aged. Medal of Honor, battlefield commissioned combat officer, Infantry Company Commander, etc. But too young to buy a damn drink. Go figure.
If (at 18) you're old enough to vote, get married, drive, buy real estate, run for political office, have your own children, go to war, sign contracts, pay taxes, be employed, or be convicted in court as an adult... you're damn well old enough to drink. Or own/carry a gun for that matter.
In past eras, 18 year old "kids" have reigned over literal kingdoms. It's about how you raise them, not some magical cutoff age. Thousands of years of human history (and biology) says that folks are already adults at 18. Sometimes a lot earlier.
In the modern West, our societies mistakenly extend the legal childhoods of our young people. But have no problem using them as cannon fodder for war. That's a bunch of crap.
Anything an 18 year old fails to do in an adult-like manner is as much a reflection of societal/parental upbringing as it is his/her maturity & experience. Treat people like children and they'll remain children. Demand that they behave as adults... and (in the main) they will. As young as you force them to do so.
I've seen teenagers assume life and death responsibilities, demonstrating fine judgement and steadfast performance under pressure. Also met insufferable 45 year old "adults" who still act like children.
Our societal problems aren't really about things like 18 year old people drinking. They are about failing to train 18 year old people to do so responsibly. And holding them accountable when they screw the pooch.