I think you misunderstand.
The restrictions in Norway are on which services private providers are licensed to provide.
It's not that many years ago that private providers were unable to offer surgeries that were covered by public healthcare at all. E.g. most private providers in Norway once they started getting licensed at all only offered things like cosmetic surgery. The first private hospital in Norway wasn't started until 1985 (Ring Medisinske Senter, now Volvat) and I remember the controversy it caused, even though it's services originally were very restricted (they were "famous" early on for being the first place in Norway you could get breast enlargements, as they were not covered by public healthcare)
It's been softened up gradually, but you'll note i you click around on the linked provided earlier that for many types of operations the only providers are either non-profits like LHL or government run hospitals - for some this is simply because no private providers have wanted to enter that space yet, but for others it's down to concerns about availability/training making the government hesitant to allow more providers, as described elsewhere.
As I pointed out in my other reply, I'm not criticizing it (at least not as long as it is regularly evaluated for whether or not it continues to offer the best treatment options, as it seems to have been).