The fact that the back substitution is not done in parallel is not important, because it uses a negligible amount of computer time when N is large, compared to the forward elimination.
This is a citation from this book (page 204) when discussing the implementation of parallel solution of linear systems using Gaussian elimination. I suspect that in practice people do parallelize back substitution and a brief googling shows that such algorithms exist. So the questions are:
- When parallel back substitution is reasonable and when it is not?
- What is the most effective parallel back substitution algorithm so far?