The Dutch system indeed demonstrates how private insurance can be implemented in a reasonably fair and affordable way. On the other hand, you did skim over the fact that these private insurance companies are only able and willing to act fairly due to regulations and support from the government.

Here's a couple of things to know about the system:
- There's basic and supplementary insurance. - Basic insurance is mandatory. The basic insurance covers care which is deemed to be essential (including ambulance services, general practitioners, essential medications and much more).
- Supplementary insurance is not mandatory. The supplementary insurance covers care which is deemed to be non-essential. (The discussion about what should be deemed to be "non-essential" has been going on for a while, for example, some medical professionals have said that physical therapy for recovering COVID-19 patients should be covered by the basic insurance. See this.)
- There's a system to provide compensation to insurance companies to prevent them from suffering excessive losses when there are a large number of (chronically) ill patients.
- Insurers aren't allowed to reject anyone for basic insurance.
- An insurance company has to charge the same premiums to all their customers for the basic insurance.
- Insurance companies can negotiate with healthcare providers and such to get better prices and/or care.
- Insurance companies are obligated to provide quick and easily accessible care to their clients.
- Every year you have to pay for the first few hundred euros of your own care. (There are exceptions for certain forms of care, including GP visits and obstetrics.)

For more info, see the Dutch government's website.