You would have a hard time convincing me that no passing/passing allowed lines are not helpful.
They are a nightmare. The double yellow lines that are prevalent in the US with very limited passing zones prevent people overtaking in otherwise clear stretches, then encourage it in shorter stretches where there may not be sufficient time or distance to complete the maneuver. I have seen some passing zones which would be sufficient to pass a tractor traveling at 20mph, but which are in no way sufficient to pass a large truck doing 50mph. By putting up a sign that says passing allowed, there will always be those that think this means it's also safe.
Similarly, there may be a long straight stretch which is divided into two passing zones, one for each direction. If you have an oncoming vehicle at the start of the stretch there would often be plenty of room to complete a pass after it goes by, but now you only have half of your 'passing allowed' zone left. Stupid.