The SCOTUS is already extremely politicized though, almost to the point of absurdity. The only real purpose of the Federalist society is to pack the whole judiciary with arch-conservative judges who will stop the progressive legal agenda. You can pretty much predict 99% of SCOTUS decisions these days (including the one that forced the G.W. Bush presidency down the country's throat) just by knowing which political party supports each side. Political campaigns obviously use the SCOTUS and federal judges in general as a major part of their platform. Even in the middle of a raging pandemic, getting relief legislation passed is taking a backseat to rushing through a SCOTUS nomination as quickly as humanly possible.
Rather than packing SCOTUS with additional justices though, I wish we were having a serious national discussion about ending lifetime appointments and imposing a term limit. It's arguably within the scope of the Constitution and wouldn't require an amendment:
https://fixthecourt.com/fix/term-limits/. Just seems to make sense on every level, considering what the SCOTUS has become. Sure it would be a political gamble for the Democratic Party, but I think their base would generally support it.