Unlike the smaller nations of Europe, which can manage an effective state level police force, these vastly underpopulated areas of the US cannot sustain such. (See for instance, Wyoming in the linked map. See that tiny population? Do you REALLY think they can sustain a robust state-wide police? Did not think so.)
Funny thing, Norway (which is nominally at least semi-part of Europe... It's complicated) has a lot of very rural areas, most likely spawning from the fact that Norwegians feel like they live in a crowded neighborhood if they can see another house.
See that cluster of buildings? I think that's actually a lodge of some sort, but there are private homes in much the same style jutting out from the cliffs along that fjord, where your nearest neighbor is across the water from you (but hopefully not DIRECTLY across, because that would be just too close for comfort). The nearest population center is at the very end of the fjord, where that cruise ship's headed, about 12-13 kilometers down the line. And that's a pretty popular area, actually!
There's actually a TV series here called "Where no one would think that anyone could live", which was specifically about finding Norwegians stuck in the little crevices and cracks across the country, because the alternative was "much too crowded" (note that the capital city, the densest-populated place in the country, has a population density of 1400/km
2. Compare with something like Chicago or Miami, at 4500/km
2 and 4800/km
2, respectively. Although Anchorage does definitely win out with 58/km
2).
Up in
Troms, where the moonshine flows and the women are nominally female, I got to listen to a presentation from one of the local policemen, who explained that for the officially unofficial designated area of "Inner Troms" (a several-thousand km
2 area where they keep the boondocksiest elements of the region) had, at any one time, a single police car on patrol. Efforts were being made to get a second car to help with the load, but funding and staffing were tight. Fun fact: Here, the common affectionate term for a buddy or pal is "horsedick", I.E. "Hey there, you old horsedick!". This has on at least one occasion caused a bit of a kerfuffle when a northerner went south to visit more civilized lands.
There's also of course
Svalbard, which is not only rural and drunk, but also just happens to have a lot of people living smack in the middle of polar bear territory. Here, due to necessity, gun laws are more lenient.
"More lenient" in this case means that individuals with a weapon ownership certificate can apply to borrow a bear defense gun from the local sheriff for a period of up to 6 months. Applications for borrowing a gun may take up to a month to fully process. Generally, weapon ownership certificates are associated with certified membership in the national fish and game organization (who have their own series of training and exams for this), but I think you can apply to get one by just providing evidence of a clean criminal record, completing some gun safety and usage classes, and maintaining a reputation for sobriety and stable mental health. Not sure on that point, as I've never personally applied (guns are FUCKING EXPENSIVE, and you can pretty much only get hunting rifles, which I'm not that interested in).
So, basically, despite being an old country with a much smaller geographic area than the US (and with a very real threat from wildlife in some areas), Norway at least doesn't necessarily stand up to the description of a "well-manned and maintained police force", while still not having a lot of guns (comparitively) even in those extra-rural areas.
All that said, my dad does still have fond memories of pissing off one of the old codgers in his area, because said codger would shoot his shotgun at the kids running around on his lawn (salt shells, which in my dad's words "Burned like hell"). But that was back in the 70's, so take it with a grain of salt.