Are you sure you mean 'pavement'? My impression from a visit to Copenhagen was of a very comprehensive network of kerb-segregated cycle paths, very wide and providing excellent continuity through junctions, but also separated from the pavements. They have created their cycle routes by taking space from cars, not from pedestrians. I must admit to have been very impressed as well, even though I am generally sceptical about segregated cycle routes, not least because of the awful experience we have of this in the UK. However, what did strike me was that their streets seemed to be quite a bit wider in the first place. I've been looking hard at main roads into Oxford and London, and I just don't think we've got enough space to do something as comprehensively as the Copenhagen network. Because even if you squeeze cars out, you still need somewhere for buses, delivery vehicles etc.
Well, now that you mention it, I'm not sure if they are allowed to cycle on the pavement, however, I saw many cyclist riding on pavement. also, as you pointed out the network of cycle paths.
Furthermore, I saw lots of cyclists riding on the high street..... not sure they are allowed to do so either. Come to think of it, I also saw the police on foot but I never saw them asking cyclist to dismount their bikes.
I see that nobody commented on my opinion that cyclist riding dangerously around pedestrians should be arrested and fined - is that because people don't agree there is a problem or just think is not a good idea? I do think that some cyclist give cyclist a bad name and in some cases motorist just take out their frustration on cyclists.
I'm convince that cyclist must help themselves to change the attitude of people towards cyclists. As a pedestrian I feel afraid of some cyclists, as a cyclist I try my very best to be on the lookout for pedestrians and I also ride at a speed that I can stop in time, in fact, it has happened to me many times when I've taken the option to stop rather than squeeze between people. And as a driver, since I ride a bike, I'm far more alert to cyclists on the road.
I do a lot of my riding on the Bournemouth promenade and everyday I see people riding at speeds that they could not possibly stop if a child crossed in front of them. Parents sometimes look in shock at these cyclist and of course, the next cyclist along get the evil look

I've come to think that these riders get a thrill out of riding fast around people, it's like a test to show how good they are...... unfortunately, it takes just a second for a serious accident. I'm sure some of those pedestrians, when behind the wheel, give the same treatment to cyclist on the road.