One take I've seen some Australian lawyers suggest is that the extent of politicisation of America's Supreme Court is an inevitable result of how highly political their constitution is.
In Australia, our constitution deals with the basic functioning of government; how elections take place, who can vote, and mostly fairly boring procedural stuff like that.
America's constitution quite famously lays out a number of very specific rights. Rights that are, by their very nature, quite politiciseable and open to interpretation. If SCOTUS is able to invent rights that they claim are implied by the written text, with the legislature unable to legislate around it, that's a problem. It becomes even more of a problem when SCOTUS decides they can infer rights that are implied by those rights which SCOTUS themselves inferred. Deciding what rights people have—or removing those rights—should be the job of democratically elected representatives, not political appointees. So the court granting a right to abortion because they say it's implied that you have this right based on the right to privacy (quite a large stretch, IMO), and that right to privacy being implied by your explicit right to due process (a more reasonable inference), is quite a silly arrangement. Better for the legislature to simply do their job.
Not that this is in any way "simple". It would require a complete ground-up rewrite of the American constitution. And that's obviously never going to happen.