The court is an expression of political power. Expressing political power through it is not stupid.
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.
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.
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.
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.
I don't think it's 100% possible to stop a determined political movement in the US from doing A Holocaust, but I think it's worth at least trying to make it tough.