Part of this appeals to me since the IL Board of Elections works on a similar principle. It is 4-4 by party and it takes 5 votes to pass a motion. It has worked well to keep an unwanted majority from putting their thumbs on election decisions.
I like the idea in theory but it doesn't work if one side is constantly operating in bad faith. North Carolina is the most notorious example of that right now. They
want a perfectly split board because they can force counties to default to 1 early voting site by just obstructing early voting decisions. Obviously this could be solved by having "default" plans adhere to a proportional formula, but still. Not that I necessarily think SCOTUS operates in bad faith, but that the general idea of a split partisan balance for any type of board/court can have its drawbacks. Especially when each side has diametrically opposing beliefs on certain subjects.
Although tbh at this point, that USSC idea could be useful for voting rights. But that is more of an example of how much we are regressing than anything else.