Pretty much. I'm insured in the public system of my relatively wealthy EU country but I still pay for a lot of stuff out of my own pocket. Not life threating stuff, that would usually be free, but still, things I need to make my conditions more bearable or for prevention, or physiotherapy for back pain, or getting appointments sooner than 3 months for a checkup.

With the ever increasing ageing population, and stagnating economy, the pressure on the healthcare system balloons while the money pot is finite, so the existing resources keep getting split more and more aggressively creating a system of winners and losers. It's inevitable when the resources are finite but the demand virtually infinite.