My understanding is that the President may choose to elevate an Associate Justice to the role of Chief Justice, but that this is not normally done. Was the choice to have the President select the Chief instead of the role passing down automatically an intentional choice? If so, is there a record of why that choice was made?
The Chief Justice of the United States can be selected either from the current Associate Justices on SCOTUS or a newly elevated SCOTUS judge. The reasons it is typically a newly elevated judge are twofold.
SCOTUS judges have become de facto politcal appointments. Even as far back as Adams granted commissions to judges that lead to Marbury v. Madison 5 U.S. 137 (1803), judicial appointments have been political. A new SCOTUS judge picked by POTUS will be in line with the views of POTUS and continue these views long after POTUS has left office.
CJ of SCOTUS is a Senate-confirmed, position. Just as new associate judges must be confirmed by the Senate, so must an associate judge being raised up to CJ. The result of this being, it is simpler to get a new judge confirmed directly as CJ, rather than a new judge as an associate, and a former associate as CJ. This is a minor reason, but the Article III considerations for Senate confirmations do play a role.
Was the choice to have the President select the Chief instead of the role passing down automatically an intentional choice?
It was. This was part of the checks and balances as well as a way to prevent "hereditary" passing on of duties. Consider the Speaker of the House. This does not automatically go to the longest serving member in the majority party either, rather, elected among the members of the House.