I have not read all answers and comments so I might have missed a link already here, but I think this is the best site for for arguments about all to do with cycling and road safety. On the right hand site you will find many internal links to posts in themes, like 'what works' or 'cycle paths'
I am not able to give you useful quotes from each of the links as they contain so much information and the themes might not really meet the arguments or more likely be just about one detail instead of about all. And he has links to other sites, often with good arguments in their own right.
So far for David Hembrow's site, from here on it is my opinion.
As a Dutch cyclist, who grew up in the time our bike lanes and paths were at their lowest ebb, I do appreciate the lanes when done well. The famous painted line, which every car driver ignores, is not much use. But when bikes are out in numbers and fill those lanes, the car drivers do pay more attention and parked cars will be rarer.
It took the Netherlands 30 years of experimenting and re-designing, and at this time there is a 'new' problem, too many cyclists for the existing infrastructure.
Separate lanes next to the road will work only when the cyclists have the same comfort and rights as the cars, can cycle on without dismounting and road design is done in such way the entrances and exits to the lanes work. Combined cycling and walking use is only possible when cyclist and pedestrians do not want to use the lane at the same time.
Bike routes away from roads might work in some cases, it will not work in all.
When the route between two main locations passes a pinch point where no work will make for bike safety, but there is an alternative route which is a bit longer but away from the cars, it might be worth investing in it.
In the Netherlands we have no cycle lanes on roads that allow cars to go 80 km/h (about 50 mph) or faster, there will often be cycle paths near the road but they might also use a different, often shorter, route.
Roads that are 50 km/h (about 30 mph) have bike lanes on road although off road lanes or near bike paths are around as well.
Most roads that are 30 km/h (about 20 mph) do not usually have separate bike infrastructure but many of those roads are no through roads for cars but allow bikes to use them to connect to other parts of town.
That makes that almost no bikes and cars need to use the same road surface without the need for bike lanes and paths everywhere. We still do have more bike paths in a small country than most big countries, not only relative to size but also in actual km/miles. While at the same time we have fewer car/bike accidents and deaths from them.
The one area where deaths of cyclists goes up is in the over 65 (or even over 75) age group, as people keep cycling and now often get e-bikes and go the allowed 25km/h while not used to those speeds anymore, if they ever have been that is. Most of those accidents are one sided, the cyclist falling, hitting something near the path or road or just dropping over when having a heart attack.