No problem, it's nice to be able to talk about this stuff!
My jaw fell on the floor when I read what you're paying in medical fees. It's bizarre that giving birth should cost that much. For reference, that's one of the requirements every insurance company is obligated to cover in the basic plans.

Single payer differs from what we have and is maybe even better, but really hard to accomplish. Here's an article that explains it quite well. The cool thing with our system is that you can make your insurance plan as expensive as you want, and you have to ability to cater it to your wishes. Do you use a lot of dental care? You can opt for an extra insurance above the basic one, to cover those costs. Don't want to get insured for care you don't need? Just get the basic plan, and pay out of pocket for your physical therapy of dentist. You can even lower the cost of your basic plan, if you have the means to pay out of pocket, by raising your own risk excess (this is the amount of money you pay out of pocket when there's a claim made, it's standard to have this at a total of 385 euro per year, but you can raise it so you pay more out of pocket, and less per month).

Hope your baby and partner are doing fine! :)