Cycles can't as a general rule keep up with cars, unlike motorcycles. There's no integrating them with auto traffic whether or not you force them into the same roadway.
Part of good separate path design is planning the intersections to prevent the sort of crashes you're describing. I've seen some designs that make sense - it's rather interesting actually what nuances go into safe intersection design. I don't have any links available offhand though.
> There's no integrating them with auto traffic whether or not you force them into the same roadway.
Roads can accommodate traffic moving at different speeds. For example, buses and trucks consistently move slower than passenger vehicles, especially up grades, but drivers of faster vehicles simply change lanes to pass them. This works on interstates where drivers of passenger vehicles are going 70 to 90 mph and commercial vehicles are going 40 to 60 mph.
Similarly, on a surface street with traffic moving anywhere from 0 to 40 mph, cyclists moving 0 to 20 mph can similarly integrate with traffic with faster drivers changing lanes to pass them.
> Part of good separate path design is planning the intersections to prevent the sort of crashes you're describing.
I've read about the designs, but the assumptions that they make do not really hold. For example, the typical "protected" intersection with curb extensions and an offset assumes that a motorist will look down the bike path to check for cyclists before exiting an intersection while moving at 10 mph. In reality, drivers aren't going to do that.
As I noted earlier, this principle works with pedestrians, because, while walking, they're moving around 5 feet per second, so seeing a pedestrian 10 feet away from the intersection is pretty easy for a driver making a turn since they really don't have to look down the sidewalk.
In contrast, a cyclist is moving anywhere from 15 to 30 feet per second. A cyclist that's two seconds away from entering an intersection can be anywhere from 30 to 60 feet away. This requires a drivers to actually look down the bike path, which isn't always going to occur. The cyclist may assume that the turning driver has seen them, but that assumption is in correct, and the cyclist will have to slow rapidly to avoid a collision.
Also, a lot of cyclists, when making use of such infrastructure, believe that they have pedestrian style right of way, meaning that they will do things like ride around the front of a turning vehicle believing that they'll stop to avoid a collision instead of just yielding.
A typical person takes about a second or so to react to something unexpected. At 10 mph, the motorist has already covered 16 feet, meaning that they would collide with a cyclist before they have a chance to even press the brake pedal.
Part of good separate path design is planning the intersections to prevent the sort of crashes you're describing. I've seen some designs that make sense - it's rather interesting actually what nuances go into safe intersection design. I don't have any links available offhand though.