(None of this is anywhere near Copenhagen)
And unless London has changed an awful lot since Wednesday when I was last there, none of it has anything at all to do with segregated paths in London. I picked on Copenhagen because it's the nearest thing Denmark has got to London.
PS - I see that, now that your version of the Dutch story is getting too difficult to defend you're picking on the other fabled success story. Let's widen the debate.
Flanders - not a great deal of segregation, most of the paths and the signage are poor even by British standards, loads and loads of cyclists.
MK - a model set of segregation (which, incidentally, I think is extremely well designed) - no-one uses it to speak of.
Oxford - almost no meaningful off-road cycle lanes, horrific road surfaces, traffic which is god-awful and not very observant - cycling is the most common mode of transport.
Segregated paths have their place. I'd be delighted to see them built along urban near-motorway like the A40 in West London, the A3 from Kingston to Guildford, the Euston/Marylebone Road. But they're neither necessary nor sufficient to increase cycling or cyclists' safety.