^^^^^^^^^^^^^^^^^^^^^^
THIS! Right here!
Cooler heads in the Democratic party (yes, there are some) will hopefully realize that once you throw open this Pandora's box, there's no closing it. So Dems boost the court to 13? Well, when Republicans take power they'll boost it to 17. Or 21.
Before you know it we'll have 35 judges on the SCOTUS and they will have become just another "political" branch.
There's a very famous SCOTUS decision (as often as I use the quote I should probably try to find it) that says "The Court has No Purse and No Sword." IOW, SCOTUS decisions are only "enforceable" as long as people generally agree that it's a good idea to abide by them. They rely on their own persuasiveness and on a general consensus that having a legal "referee" is a good idea. IOW, I will support the decisions I don't like that benefit you, and I expect YOU to support the decisions that you don't like that benefit me.
Once that agreement is broken, the Court no longer has any power because jurisdictions will start to realize they can ignore SCOTUS decisions with impunity. I mean, what's the SCOTUS going to do, send the SCOTUS police out to arrest people? Send the SCOTUS airborne division to enforce their decrees? Deny funding for this or that agency? No, because they have no such power.

