All companies offer completely exchangeable plans and are only allowed to take age, municipality and desired copay into account when calculating your premium. Every resident of Switzerland is also obligated to have this basic health insurance (if you don’t, the government just picks a random insurance for you and signs you up retroactively).
I would say it’s a great system…but Swiss health care costs are also among the highest in the world (and rising steeply), so it’s not a silver bullet.
To be fair, this particular system is probably not to blame for the high costs, but it also didn’t prevent them (though it leads to a bit of innovation around e.g. telemedicine, which is great).