It's a road system designed for humans, and with current tech, you'll always have issues chasing the long tail down. Though I'm fairly sure self-driving is still statistically better than humans behind the wheel, especially distracted humans as the information age has made us.
The more immediate solution is white-listing safe roads that have sane paint lines and are relatively straight-forward roads. That way, the chance of the AI getting it wrong is drastically reduced. This covers most highways where you get the most out of self-driving systems anyway. Bonus points if you can automate this decision-making with recent satellite imagery.
Another analogy could me made to data entry: you could allow free-form text input and try to process all of the long tail of unexpected inputs, or else set out a format that the data has to follow and enforce validation at the input.
The need for lines is only a temporary crux. AI systems will continually improve until the white lines are guidelines only. There are lots of other factors in an image that can be used to deduce where the lines should be.
But there will have to be handling of uncertainty which humans have to do too, simply just slowing down (not sharp braking) will help most cases.