I have wondered why the checkers are set up on the points in the way we're familiar with. I imagine there is some historical explanation. Has anybody shown (presumably with computer simulations) that this makes for a better game than any alternative configuration? Or that the number of checkers and points is optimal?

I don’t know the history or if it is the most optimal setup but a few thoughts:

1. Having eight checkers within one die roll of your home board points plus bar point allows for a fairly quick development of a prime and/or home board points.

2. Closely related to the first point, having two back checkers widely separated from the rest yields a situation it is simultaneously true that you are under pressure to get them moving before they are blocked or attacked and you have very limited options for safely moving them.

3. Checkers on the midpoint simultaneously provide a safe landing spot for the back checkers, but only on either a lucky roll or after exposing them to being attacked and provides additional checkers that can be brought into play for attacking or priming in your home board.

There may be better setups, and there are variants such as nackgammon that do use such alternative arrangements, but the traditional setup seems pretty well thought out even if it is not optimal

The board with 24 points and 30 checkers dates back at least to the Roman occupation of Palestine around the time of Christ. Various combinations of initial position, # of dice, and rules for movement evolved over the centuries.

Our current setup dates back at least to the late 17th century and perhaps earlier. It replaced tric-trac as the most popular form of the game in the early 19th century. The doubling cube and chouettes were invented in the 1920s and created an exciting, fast-paced game for gambling, which helped fuel an enormous burst in popularity.

I don't know what an 'optimal' setup would be, or how you would prove that any particular setup is optimal.