The only people who persistence hunt still are the people who didn't find a better approach. Be it that they don't need a better approach (which is fine. Means they're optimized) or that they simply spend.so much time hunting that they don't have the excess time and resources to experiment with new approaches
I also think it depends on the environment. I can imagine ancient humans persistence hunting across the plains of Africa. I have a harder time picturing it in rain forests or the forests that used to cover most of Europe.