You drive (or ride) next to the side of the road, and faster traffic overtakes by passing nearer the centre of the road.
"Second, in LA, as I think it should be everywhere, most traffic is neither fast nor slow but just flowing with the predominant speed."
In the UK, many large trucks travel below 70mph, which is the general speed limit. Most, but not all, cars will travel either close to 70mph or above it, so it is hard to state there is one 'predominant speed'.
"The slow traffic goes to the right of the driver"; there's your conceptual problem, I think. Traffic going slower than others cannot decide to go to one side or the other of the faster traffic, because that traffic is behind it, about to overtake. So everyone should keep to the slowest lane, if there's room in it, so that whatever the relative speeds of traffic behind, they all get the chance to overtake where possible. If you're going at 70, and there are 2 cars coming up behind you, one at 75 and one at 80, then you should be in the left hand lane, so that the 75mph car can take the middle, and the 80 the right (British sides of the road). It is not easy to judge the relative speeds of all the vehicles behind you and then decide whether you really need to get in the left hand lane; it's easier just to make it the rule.
"That is what rear-view mirrors and side-view mirrors are for. We watch out as we drive. " As I said, the problem is that overtaking on both sides means you have to look for cars that are beyond the areas your mirrors cover. If you've just overtaken a car in the middle lane, a car in the far lane will have been hidden from you for a considerable time (especially if the one in the middle is tall, like a minivan, SUV or truck). They may never have been visible in your mirrors. You end up having to turn your head to look left and right, and lose the peripheral vision of what's in front of you. It's not as safe.
"In LA, the traffic weaves in and out." But you said you get ticketed for that. Which shows the system cannot be working that well.
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