"Traffic laws", I assume these people will treat them as seriously as our immigration laws.

But let's discuss the difficulty of driving having lived in the US most if not all of our lives. It's difficult enough traveling through different states where laws are similar and yet you need to adapt. For example try driving in NY after learning to drive elsewhere, it's a whole different animal. I've logged coast to coast and international miles; Canada was a pleasure. 

Now let's take an illegal immigrant who has little experience with our culture and language. They are already a fugitive from the law and a quasi legal drivers license doesn't change that. If involved in an accident they have that motivation to flee (especially with ICE being more active). Yes, the process of getting said document is a basic intro to driving here but it's not enough. When we get right down to it they are a risk that we don't need on the roads.