This chart shows how many people use the overtaking lane when it is about to stop, as a function of how busy the road is. I'm talking about say 500 metres before the lane finishes, so not including those drivers who squeeze in at the last second narrowly avoiding an accident.
When hardly anyone is on the road, everyone uses the lane that isn't stopping (I'll call it the right lane here, but it could equally be the left lane in your country). And when there is a huge traffic jam for miles, generally both lanes get used equally (and are usually stopped).
The interesting part is between the two extremes. As traffic gets a little heavier there will naturally be some people using the overtaking lane. As the traffic gets heavier still the amount will increase until it's split fairly evenly, but most people are still able to go at the speed they want.
At some critical point the traffic flow rate will slow due to too much traffic. At this point something very interesting happens. Suddenly people stop using the left lane as much and instead choose to queue in the right lane. Once people start to do this, others feel compelled to do the same as the left lane is almost empty and it would be "cheating" to use the left lane. You still get the odd person spotting an opportunity to save a few minutes and use the left lane.
Once the situation gets really bad, when traffic is almost stopped, suddenly people start using the left lane again, it will fill up until both lanes are full of stationary traffic.