I have to disagree with much of your post. I don't think your in-laws' experience is that close to typical.
Norway's system may be superior, I'll take your word for it. But honestly speaking, it SHOULD be. Norway's problem is much more manageable because Norway is quite a bit wealthier than the US (53k per capita GDP vs 45k) and has a population the size of Kentucky.
Kaiser Permanente, which is a single insurance provider in the US, has twice as many members as Norway has people (and rates extremely highly for quality of care, by the way).
Have you ever asked your in-laws why they go to a doc-in-a-box and don't pick a primary physician? Every insurance plan I've ever had has let me pick a primary doc and see them any time - I've had the same doctor for 15 years.
Most people I know have "their" doctor and stick with them until they decide to switch or a change of insurance takes them out of their list of approved providers. The only people I know that don't have a primary physician are younger people who haven't had a reason to see a doctor since they left their parents insurance.
Also, maybe I haven't been paying attention, but I've never seen an employer require a doctor's note for sick leave of any length. Maybe companies put language to that effect in their employee handbook in case they need it to deal with abuse of the system, but in 20 years working I've never known of anyone being asked for a note.