Of course there are cars
though cycling is also common and the public transport network is very good so people do use that. But certainly a lot of people drive; Germans love their cars. Electric cars are becoming quite common too but most of them here seem to have the noise that activates below a certain speed.
And I haven't signed it so no, I don't allow him to walk home alone.
To be fair, this is not offered at every Kindergarten. The one he goes to right now is a two minute (adult pace) or about 6 minute toddler pace walk from our front door. There is one road to cross which has a marked crossing (not a zebra but everyone treats it like one) and very little traffic, because the entire small area that we live in is essentially a Q-shaped cul-de-sac with one road in or out, so nobody drives around the Q unless they live here. For many of the houses, they are on the inside of the Q, so you can get to them simply by walking through a park and not crossing any roads at all. I imagine the parents who do sign for their 5yo to leave alone live in one of these houses. They also let them out at about 1 in the afternoon, so no rush hour traffic and good lighting at all times of year. And, as someone else pointed out, when they do walk home at 6yo (which is more usual) they are generally in groups with other children, some of whom will be in the older classes aged 8-10.
In Germany it is a rule that you have to send your child to the most local school unless there is a very good reason to send them somewhere else, so there are very few parents bringing children by car because you don't need to; schools are not mobbed by cars, parents generally walk or bike with children in the first class until Christmas and then traditionally they walk in small groups. In January and February there are signs up reminding drivers to be aware of children and the (ridiculously expensive) school bags you are encouraged to buy all have reflective patches on, governed by some kind of standard. Brightly coloured, reflective coats are also encouraged and children are given free reflective bands, jackets, stickers, dangly things to attach to their bags/coats/bikes etc commonly in the first few weeks of school. There is no rule of black coats only like in the UK.
I don't think Germany has a much worse road safety record than the UK (I know it is slightly worse overall, but very similar especially in comparison to countries like Italy, Greece, Romania) but it is hard to find detailed statistics to compare since the UK left the EU because they tend to be left out of comparisons.
TBH most accidents I hear about seem to involve children aged 12+.