> I also have much better visibility at junctions on the main road instead of on bicycle lanes that are closer to walls and hedges and have 3 or 4 meters less of buffer between me and incoming cars from the right. I'm also less visible to them.

More anecdata: I take the bike when I can, and I have had motorists run into me a few times.

Every single time has been on dedicated bike roads.

Don't get me wrong -- I have had many, many more near misses on regular roads, but regular roads are built in ways which make it easy to convert impending collisions into near misses. Bike roads tend to not have those margins.

Before dedicated bike roads can be considered a solution, they must be built in ways which make me feel safer when I choose them.

How did motorists end up on dedicated bike roads?

Often these "dedicated bike roads" become not-so-dedicated at junctions. Also motorists frequently ignore painted lines marking bicycle lanes. (You can argue for physically segregated bike lanes instead of painted lines, but as a cyclist I won't use physically segregated bike lanes unless I know how they end, because all too often you get a "bike lane to nowhere" with no way to get off it).

Yes, and suddenly you're in a tunnel frequented by characters you're likely to find in a crime thriller who like to find out-of-the-way places to practice their craft.

So you mean dedicated bike lanes, I think. Dedicated bike roads implies physically segregated to me.

An (anti)pattern I often see is a road that's physically segregated for plain road, but then merges into and out of the main roadway (sometimes becoming a dedicated lane) for junctions.

It's so that drivers would see the cyclists in junctions. If the bike path is separated until the junction, it's common that drivers don't pay attention at all to what happens on bike paths and turn right into crossing bike traffic. What makes things worse is that usually there are bushes, placards, bus stops and others between road and bike path, all of which block visibility and grab attention.

I like your optimism. I've heard that in the Netherlands, the solve this problem by having a red turning arrow when people (on foot, on bike or in cars) are allowed to go forward. So in drive-on-the-left terms, vehicle traffic is allowed to go from the south to the north or east or from the east to the south. Since people who are driving cars from the south and want to turn to the west are obliged to stop, there's no possibility they'll unintentionally charge into people walking or riding bikes across the western entrance. The disadvantage is it requires four cycles not two, and therefore reduces the time pedestrians can cross.

On Albert St and Swanston St in (East) Melbourne, the separated lane stops at intersections so that cars can use the bike lane to turn left. People riding bikes are supposed to give way to people driving cars and then filter around the stopped cars into the bike box ahead of the cars. I never really feel safe using the Albert St lane for this and other reasons. Fortunately I have other options.

You ask great questions and they have been answered by someone else already! These dedicated bike roads do not have grade separated junctions, so in intersections sometimes motor traffic has to use a part of the cycleway, and sometimes cycle traffic has to use part of the regular roadway.

Yes, you can do 30-40 on the bicycle paths, and bicycle paths are not used by pedestrians.

You can if they are maintained. Most dedicated bike paths around me have ripples in the surface from tree roots and have never been resurfaced since they were built. Using a road bike with skinny tires on them is bone jarring at low speed.

Is that in Denmark?

No, the United Kingdom.