The SC should be formed by lot from judges in the lower courts, every so often (every session might work OK).

We form other courts by lot. Constitutionally, there just must be a Supreme Court. It doesn’t say how it should be composed.

Packing is a band-aid, and likely to be unpopular. This is a fix with a less nakedly-partisan result, so should be easier to sell.

Do you really think that if you packed the court, there is anything you could do to prevent the other party from doing the same thing the next time they're in power? Your plan would have to be to prevent them from ever getting back into power, and that's a civil war.

On top of that, Clarence Thomas is the oldest person on the court and Alito is only two years younger. By the end of the next Presidential term they'll both be in their 80s. You don't have to pack the court, you just have to be in office for the term or two after this one.