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I think, like Amsterdam, Copenhagen used to be car dominated too. All old cities were "built for humans" and could get there again with different mindset (planners and public).
It depends on what you mean. København and Amsterdam are today far more car-dominated than ever before, just not in the centre. The motor traffic that upset people so much in the 1970s was actually small in volume compared to what there is today, but was new to the small, tight centres, and obviously, as everywhere in Europe, caused a lot of road traffic casualties. Campaigners managed to avert the wholesale destruction of traditional parts of the city (which was done in London for the Westway, for instance), but the upshot was that through motor traffic has now merely been moved to the motorways on the outskirts, as there has been a lot of road-building, creating huge additional capacity, and it's not as noticeable in the centre. Both cities have developed a lot in the last couple of decades, and along with that have added ring roads, a lot of residential car parking, and the need to travel has increased massively.
Both the Netherlands and Denmark have changed their economies on the model of surrounding larger countries, i.e. much more centred on the larger agglomerations, destroying the traditional model of, for instance, small farming operations, which are today replaced by large agribusiness. Perishable produce needs to get to the borders quickly, and all those lorries have to be driven somewhere. As in most parts of Europe, people can increasingly not work locally, as employers and work are not available there any more (and this was a trend that existed even before computing became so prevalent), meaning many have to commute huge distances. Modal share of motor traffic has increased a lot in both countries and is seen as a symptom of affluence, as both countries used to be quite poor (read: with more even wealth and income distribution) well into the 1960s.
It's really much the same story everywhere. Good work has been done by Jan Gehl and co. in the centre of København, e.g. reducing available car parking there by 1% each year, but overall the picture has become as dire in both countries as anywhere else. The cities retain modal shares of cycling of around 20% (don't believe the inflated figures of 40-50%, they're either for selected central areas or don't count walking), which is good, but it's largely due to the absence of public transport. There won't be an underground railway network in Amsterdam because of soil conditions, but Københaven has been building one (https://intl.m.dk/) and it's already eaten into the modal share of other modes, as obviously it's designed to do.
People tend to over-emphasise the small positives and don't look enough at the big picture. I don't want to be a party spoiler, and obviously I'm happy that @ltc had a nice time there, but it's important to avoid becoming distracted from the continuing march of motorisation by such positives.
I spotted someone watching South Park as they were cycling through the Greenwich Foot Tunnel last week. Wild.
I've spent the last few days in Copenhagen, thoroughly enjoying a city actually built for human beings. I'm not really looking forward to the hostility of a London commute tomorrow!