Packing the court is unprecedented, and as soon as anyone did it, they would both do it continuously. It would also outrage the other party and make the first to do it more likely to lose the next election.
So you would get to pack the court for the rest of your current term before the other party gets back in and packs it the other way, and thereafter lose the courts as a check on the party in power forever because the first thing a party would do when they get into power is pack the courts.
It's a monumentally stupid idea.
I see no reason we can't have hundreds of supreme court judges.
As with partisan gerrymandering, packing the court cannot be the only step.
It would need to come with a commitment to a package of difficult to undo (i.e. amendments) reforms. SCOTUS term limits, preventing the Senate from refusing to even consider nominees, bans on justices receiving gifts (https://www.propublica.org/article/clarence-thomas-scotus-un...), revocation of Presidential immunity, etc. You pack the court with an explicit promise to largely return to the old status quo when it's fixed.