1. The 15% of income has a cap. It's something like after 60k EUR in wages you don't pay anymore. Also, only 7.5% comes out of your paycheck, the employer pays the other half. When I was there a few years ago I was self employed so I had to pay "both sides". It would've worked out to roughly 750EUR/month for health insurance which had _0 deductible_ and _0 coinsurance_ for doctors visits or ER care and would've covered my entire family no matter on my children I had. Compare that with a typical HDHP family plan offered in the US and you're looking at $400/mo in premiums, with a $3k deductible and max OOP of $6k. The final cost is comparable.
2. The 15% is only if you participate in the public system - the private is not tied to your income.