film techniques - Why is director's name shown last in the title sequence?

Well, I can't answer your question (I don't know why the director is placed last in the title sequence) but one could ponder the question a little more.

The serial position effect states that we best remember items that are presented either first or last in a sequence. So, in the opening credits case, it shouldn't matter if you are presented first or last.

However, my own experience is that you don't really pay attention to the first part of the opening credits. This is when people still are fumbling for their seats in the dark or argues about who should have authority over the popcorn during the film. From that point of view, if I were the director, and I wanted to have the best exposure, I would choose to have my name shown at the end rather than the begining.

Contrary, in the end credits, the director is shown first. This would also seem like a good thing for the director given that people very seldom watch the credits to the very end.

As a sidenote, there are other fields where the sequential order in which people are mentioned is a source of heated debate. Take, for example, authors in scientific papers. Here's an excerpt from the article "Author Sequence and Credit for Contributions in Multiauthored Publications":

The situation in our area of research—the ecological and environmental
sciences—has changed in recent years. Following informal practices in
the biomedical sciences, the last author often gets as much credit as
the first author, because he or she is assumed to be the driving
force, both intellectually and financially, behind the research.
Evaluation committees and funding bodies often take last authorship as
a sign of successful group leadership and make this a criterion in
hiring, granting, and promotion. This practice is unofficial, and
hence not always followed, meaning that sometimes last authors
“mistakenly” benefit when they actually are not principal
investigators. Moreover, there is no accepted yardstick in assessing
the actual contribution of a group leader to given scientific
publications, so interpretation of author sequence can be like a
lottery. Hence, one really does not know if being last author means
that the overall contribution was the most or least important.