Dane here, Denmark isn't actually that rich. We were probably the worst of the Nordic countries in recovering from 2008, and our GDP per capita has been stagnant ever since. People here overstate how wealthy Nordic countries are, as well as how expensive the "Nordic model" actually is. Stuff like universal healthcare, free education, and other public services aren't any more expensive than their privatised counterparts (quite the contrary is some cases), they're just different ways of distributing resources. You don't need to be an oil state to do this stuff (the only ones who got really rich off oil is Norway, and we hate them for it), you just need a developed economy, and the Nordic countries do not benefit more from imperialism than any other western country (and frankly, the idea that imperialism is some universal net positive for western workers is false. Workers have suffered immensely from the decline of industry, globalisation, etc.).
As for the problems, and there are plenty (though all the ones in the OP are terrible) touches on some of it. Wages in the Nordic countries are very high, and prices are equally high. The only sectors that are really competitive are either the ones that benefit from our educated workforce or the ones that simply cannot be anywhere but here. Our tech advantage is slowly dwindling (thanks in part to the terrible policies of our neoliberal overlords, I'll get to that), and the caveat of having a highly paid, educated workforce is that if you are not highly paid and well-educated you can hardly afford to live. There was a time where a "minimum wage" job (we don't actually have a minimum wage, it depends on the union) barely paid more than unemployment benefits - the reason of course being that benefits were set at a level which provided a minimum sustainable living, and the minimum wage jobs were also at that level - and the reaction of our dear leaders was to lower benefits to something less than liveable and forcing every unemployed person to accept any shitty job within a two-hour drive (each way). Also, because of these high wages, and because Danish workers (rightfully) refuse to accept jobs that have unliveable wages in order to be "competitive", we are highly reliant on foreign workers to do the shitty menial jobs that we can't or won't do.
As I have alluded to, Denmark has suffered from the same neoliberal turn which has hit literally every other country in the western world, and it has done its very best to destroy all the lovely things workers and unions have fought tooth and nail for in the last century. I can't blame all of this on our politicians, a lot of it has to do with globalisation and the international market, but it can't be denied that every politician who isn't a fucking socialist is a neoliberal traitor who deserves to be hanged (especially the socdems). One example, around the turn of the millennium, is the "rebranding" of our welfare system by the Liberal party into what they called "Flexicurity" (yes, in English because they're soulless, corporate cunts who have been brainwashed by Americans), which basically meant using our rapidly declining unemployment benefits to prop up shitty practices and terrible job security of our corporations, while also harassing unemployed people into taking shitty jobs, as I described above. This failed massively, of course, because our politicians are fucking idiots who can't manage an economy beyond one term and who only care about amassing enough favours and golden handshakes to retire in wealth and comfort once they are inevitably hounded out of office.
IMO, the policies of the "Nordic model" - high wages, socialised and well-maintained public services, and strong unions - are all good things and something socialists all over should aspire to achieve, but it just isn't sustainable under a capitalist system and world economy. The socdem utopia is impossible, you need socialism.
