I would assume something like that would just be a way of selling it to the public without opening oneself up to accusations of blatant partisanship, while also avoiding setting a shitty precedent.
Like sure, the next Dem president could just add two justices. But then there's nothing stopping the next GOP president from adding two more once they assume power, and then just continually one-upping one another.
I'm of the mind that court reform should be more about divorcing the judiciary from the executive branch. "Gotta vote the party so we win SCOTUS" is a pretty lousy spot to be in.
That being said, you're probably right that a scheme like this would need a Constitutional amendment to work, and I don't know how you'd account for third parties. I certainly wouldn't expect it to just say flat out "Democrats get 5, Republicans get 5" because either party could easily die off.
