> In areas with painted cycle lanes, the drivers understand that in this situation they are supposed to watch for cyclists, give way and then cross into the "right turn only" lane on the cyclists' right, instead of fuming and raging because a cyclist dared to follow the signage.
While this works to some extent when a right turn only lane is present, this actually sets the cyclist up for a right hook when the right most travel lane can be used to proceed straight through the intersection or turn right. In that case, the bike lane is still painted to the right and leads to the situation where a motorist making a right turn is to the left of cyclist traffic going straight through the intersection.
> [I]n the US I think [that painted lines are] still useful as a way to teach drivers how to handle having cyclists on the road.
The problem in the US is that they paint lines in such a way that there's insufficient lateral space between the cyclist and motor vehicles. Most US states have passed laws requiring motorists to leave at least 3 feet between their vehicle and a cyclist.
In the case where a general purpose lane is 10 feet wide and the adjacent bike lane is 4 feet wide, you end up with a siutation where it's not possible to leave 3 feet of distance between the motor vehicle an and the cyclist. A typical larger vehicle is about 7.5 feet wide from mirror to mirror. Centered in a 10 foot wide lane, they have 1.25 feet on each side.
A cyclist is about 2.5 feet wide. 2.5 feet centered in a 4 foot wide bike lane leaves 0.75 feet on each side.
0.75 feet and 1.25 feet add up to 2 feet, which means that the distance with both the motorist and cyclist centered in the lane they're in is not sufficient. This doesn't account for moving side to side within the lane for either the motorist or cyclist.
I think your calculation of car sizes is a bit wide. I think most cars in the US are around 6 feet wide. Even large minivans are only around 2m. Granted, the mirrors add width and some drivers add excessive dongles on the edge of that, but conscientious drivers of wide vehicles should already be accustomed to passing slow moving vehicles more carefully. In addition, in the places where there are proper dedicated cycle lanes, the lanes are painted inside a full-width shoulder, with space to spare on both the left and the right.
I found there were quite a few stretches of road in Florida, for example, where there were 3 or 4 lanes of high speed traffic going parallel to a painted cycle path in the shoulder. It wasn't the most relaxing place to ride, but it still felt safer than going down some of the highways and arterial roads in other states where there were few (if any) cycle paths, simply because the drivers had more visual aids (signage plus lines) to tell them what to do when they saw a cyclist. I felt more confident cycling even in other parts of Florida without the cycle lanes because despite the drivers being fairly inconsiderate, at least they didn't visibly panic when they saw me there.
It is important to compare like with like, though. A "cycle path" which is just a bit of different-colored paint in the gutter of an existing traffic lane is pretty much useless. But if the painted cycle path is explicitly painted in what would otherwise be a full-width shoulder, I agree with other commenters here that it allows more flexibility to the cyclist than a separated lane (e.g. in turning left without needing to do a pedestrian-style hook turn) and it has the side effect of teaching drivers how to more carefully consider other traffic.
I really think a lot comes down to driver education. For example in areas where there is frequently slow farm equipment or horse and buggies on the main road, drivers have learned how to share the road, so it feels safe to cycle when there is no cycle path or even no shoulder at all. Unfortunately my experience in a lot of the US is that most drivers don't know how to deal with cyclists, so they'll ignorantly tailgate, cut you off or abuse you just for following the road rules. I'm not sure if that results in more casualties, but it certainly makes the experience of cycling more fraught, which means less people will want to cycle, so there is a vicious circle of increasing driver ignorance. I think painted lines at least provide some antidote to that.
> I think your calculation of car sizes is a bit wide. I think most cars in the US are around 6 feet wide.
You're not including mirrors in the width of the vehicle. Typical exterior mirrors on passenger vehicles extend out about 6 inches from the body, so that adds a foot to the vehicle's width. My VW Golf Sportwagen is about 7 feet wide mirror to mirror. My Honda Odyssey is about 7.5 feet wide mirror to mirror. I've measured both vehicles by dropping a string from the edge of the mirror housing down to the ground, and marking it on both sides and measuring the distance between the marks. Take a look at the interactive graphic towards the bottom of the page by Cycling Savvy[1]
Commercial vehicles like tractor trailers and buses are 8.5 feet wide at the body. Their mirrors extend out further, meaning that they're close to 10.5 feet wide mirror to mirror.
While this works to some extent when a right turn only lane is present, this actually sets the cyclist up for a right hook when the right most travel lane can be used to proceed straight through the intersection or turn right. In that case, the bike lane is still painted to the right and leads to the situation where a motorist making a right turn is to the left of cyclist traffic going straight through the intersection.
> [I]n the US I think [that painted lines are] still useful as a way to teach drivers how to handle having cyclists on the road.
The problem in the US is that they paint lines in such a way that there's insufficient lateral space between the cyclist and motor vehicles. Most US states have passed laws requiring motorists to leave at least 3 feet between their vehicle and a cyclist.
In the case where a general purpose lane is 10 feet wide and the adjacent bike lane is 4 feet wide, you end up with a siutation where it's not possible to leave 3 feet of distance between the motor vehicle an and the cyclist. A typical larger vehicle is about 7.5 feet wide from mirror to mirror. Centered in a 10 foot wide lane, they have 1.25 feet on each side.
A cyclist is about 2.5 feet wide. 2.5 feet centered in a 4 foot wide bike lane leaves 0.75 feet on each side.
0.75 feet and 1.25 feet add up to 2 feet, which means that the distance with both the motorist and cyclist centered in the lane they're in is not sufficient. This doesn't account for moving side to side within the lane for either the motorist or cyclist.