I've never understood this attitude to be honest, unless I'm missing something?
OK so Biden decides to stack the court, put in 6 new liberal judges so it's 9-6. Overturn this ruling, ratify many more. Sounds amazing.
But then....what happens when the new Republican president comes in? Are they not going to stack the court?
It's just a very very temporary plaster.
Let us take the other tack. The solution is voting. You have to vote for Democrats, who as a party respect the sanctity of institutions, so that the ideological balance of the court is changed.
The current court is 6-3. The conservatives can afford one death with no problem. The oldest conservatives are 74 and 72. Rich people with good healthcare in a first world country have at least 10 years more. So, you have to hope for 2 deaths in the next 10 years in a rather special set of circumstances.
1. You have to hope the Republicans never get the senate+president combination once in the next 10 years. That is unlikely, bordering on impossible, given current numbers and recent history (it has happened 10 out of the last 22 years). If it happens even once, they retire then and the plan has failed. Abortion remains illegal for at least 40ish years.
2. Let's assume, breaking all previous political logic, that the Republicans never win the senate+prez combination for the next 10 years in a row. Now, the actuarial tables smile upon you and both die. Let us hope the Dems have unified control (senate+prez) at this time, something that has happened for 4 out of the last 24 years. You act more effectively than any Dem since LBJ and get 2 replacements. These replacement Dem judges - who are all institutionalists by temperament - will now hear a case, thrown out (and hence delayed) by every level of lower court, about lack of access to abortion. Note that if the delay is long enough and the child is born, the case never gets heard. So you hope you get the perfect woman, who knows very early that she has a baby but does want to abort it, and her case reaches the court and its 5 Democrats. These Dem institutionalist judges now have to overturn precedent (Dodds 2022) and again find a right to abortion.
I don't know the probability of all these things falling into place. I'd guess substantially less than 1%. It is 4% just for going the GOP never get the Senate+presidency, and that's without taking into account the democrat and death probabilities.
I think a cyclical legality of abortion and gun control, with them being illegal for the majority but legal for a substantial minority of the future (which would be the result of court-packing, since the law would just reflect the elected senate/prez of that moment), is a better outcome than praying for a very implausible series of events.
Of course, for the same reasons that they haven't done anything about abortion in the many years of rule they've had since Roe v Wade, the Dems won't even consider something like court packing.