The problem is the size of SCOTUS in our increasingly complex and diverse age. One vote either way in a 5 to 4 decision is perceived as partisan, or a coin toss. Either way it is highly suspect if not illegitimate. The next nominee may flip it the other way, hence our horrendous nomination process. A justice arrives damaged goods, and stays damaged in the public view, further damaging the credibility of the court. The court is not fair because the court is not balanced.
Solution: Expand, not pack, the court. A traditional jury of 12 plus 1 to break ties would probably be accepted as a tried and true number by the general public. And any one justice would be far less critical in a larger court.
Furthermore: NO MORE 5 TO 4 TOSS-UP DECISIONS!