Statistically speaking, for white and black, what is the last piece moved from its starting position, and why?
I think a good approach to this is to see what pieces most likely move first.
Central pawns normally always come out.
The bishops and knights come out early
If you castle early, one of the rooks plus the king will have moved
The other rook is sometimes left stationary unless there is an open file.
The queen normally gets into play.
Since you want to keep the king safeguarded, especially if castled, I would say most players would try to move the pawns in front of the castled king last or leave them on their original squares.
There are so many factors that would affect that. Player strength, for one, as weaker players tend to play heavy pieces first (beginners always have to be told not to push their rook pawns and bring their rooks out in front of their pawns).
Next, the opening choice affects it strongly, because that can dictate both castling and pawn structure.
What's the purpose of the question, aside from idle curiosity? Is there a principle you're aiming for?