IMO the most distinct parts of the Swiss health insurance system is that (1) copay is obligatory but limited (i.e. healthcare isn’t free but it’s not expensive either), and (2) it’s individual, companies cannot pay for it, so there’s no US-like extreme benefit of having a good job.
Due to the regulations it is not a big run to the bottom
It isn’t really bargaining power of the pool, but the risk assessment of the pool you are in. Being in a hodge lodge personal pool means you are sharing risk with people who will have more expenses. That’s why Switzerland throws everyone into the same pool, so no crème low risk can be siphoned away.