Agree with a lot of what is on this thread.
Most of the cycle paths I have come across in the UK (Outside of London) are suitable for shoppers, slow commuters, or children for sure.
Looking at the wonderful photo from Denmark, yes I would use that for sure, well maintained, free of debris, and no need to stop, unless you are giving way to another cyclist - perfect.
I have recently been riding in southern Spain, and despite the traffic not being that heavy there, they have some wonderful segregated cycle paths, alongside, and then going under dual carriageways, the first time I rode that route I missed their existence, and continued on the road (Which to be fair was fine) but after that I have used the paths, and they are a breeze, and so much more relaxed.
Additionally they have some well tarmacced canal paths which are in 99% amazing condition, and also WIDE, so no needing to pull in and wait for oncoming traffic, or struggling to pass slower traffic - there are km and km of it, it's a totally different world - and that's without mentioning the weather and tolerant motorists.
Cycle paths in my town, and in this culture driven by tabloids, are divisive at best, dangerous at worst.
There are some big wide roads here that were perfectly fine as they were, but they have decided to put cycle paths on them.
The issues are now that some of them have apples falling on them, as well as debris now pushed into them by traffic, and seemingly are never cleaned or swept.
Another stretch alongside a 60mph road which is perfectly wide enough for cycles and cars, we now have a lovely path, BUT we have to keep braking and giving way/checking for traffic coming out of the properties/establishments on that side of the road.
I'm fairly sure in other countries it is the cycle lane that has priority and traffic pulling out has to check and give way no?
Once coming down there, there was someone coming to pull out, so I braked, and eased off, but they waved me out, which is lovely, but they had no need to, and it's not something you can or would assume would happen.
And of course having built all these cycle paths here to great levels of publicity means that all the 'why aren't they spending money to fix the potholes instead / I've seen one cyclist use t in 4 weeks' people love to crawl out of their swamp and add their hatred to the pot.
I can't see any seismic change in cycling infrastructure that actually works in the UK to be fair, certainly not in my lifetime, maybe at the end of this century or into the start of the next one.
For that to happen the tabloids will need to be disbanded, a really strong and respected government will need to be in charge, and our inhabitants will need to start forming opinions for themselves, as well as not being so reliant on cars.