I'm not familiar with the german system... is it private or public insurance?
As for US employers paying for everything... yes it's common. It used to be that they'd just cover everything via a 'PPO' plan with minimal 'co-pays'. Usually you'd pay $5-15 for a GP, ~$50 for urgent care, and ~$100 for an ER visit.
These days, many have switched to a 'High Deductible' plan, where the insurance comes with a 'max out-of-pocket'. After you've paid that amount, then everything is fully covered, but nothing is covered until you hit the deductible.
My current company has this plan, but puts the entire 'max out of pocket' value in what's called an 'HSA' (healthcare savings account). This money grows tax free and will eventually turn into a retirement account. So, if you have no health issues, then this becomes a free income stream. If you do have health issues, then you just spend this money every year and then insurance takes over and pays for the rest. This is common in the tech world these days... not sure about other industries TBH.