His affability will probably be valuable in his role as chief justice. The justices' workload is intense, and the Washington winters long. As chief justice, it will be his responsibility to make sure that the place, in its many aspects, functions.
Because the justices have lifetime tenure, and are appointed, not elected, the Supreme Court has been referred to as the least political branch. The chambers of the nine justices have been likened to nine separate law firms. But in order to author a majority opinion, a justice needs four other affirmative votes (in the ordinary case). The process of persuading others to join an opinion invariably leads to "intra-court" politics. Some are better at this persuasion, this form of politics, than others. Rehnquist is one of the best, if not the best.
For example, he has recognized that early circulation of a hard-hitting draft opinion may be more effective in securing and solidifying the votes of other justices than might be a more gilded, but late-arriving opinion, suitable for dissection by law review students everywhere. I remember a case in which he began as the sole vote for a particular result. He circulated a draft opinion, got a few relatively favorable comments from other justices and circulated a redraft. The process continued, each redraft faithful to the constitutional principle espoused yet bending to embrace changes suggested by other justices. His majority opinion was published with only two dissents.