They do that too, a lot in fact. Most of the cases that request a certiorari are denied.

https://supremecourtpress.com/chance_of_success.html

And in the majority of those cases the SC does only instruct the lower court on that specific case, refraining from creating new law as much as possible.

France is a "civil law" country. Courts there cannot "make new laws", they can only invalidate them. (And as far as I know this applies in general to all civil law countries.)

> France is a "civil law" country. Courts there cannot "make new laws", they can only invalidate them. (And as far as I know this applies in general to all civil law countries.)

The German Supreme Court has, on two occasions, declared new constitutional rights: the right to informational self-determination (when deliberating a census process law) and the right to integrity of data processing systems (when outlaying voting computers). I don't know if that counts though since technically they argued that other constitutional rights implied these rights (but weren't mentioned explicitly because the German Basic Law was drafted in 1949).

Well, clearly both parties seem to have expectations that the court will rule on controversial matters like abortion. The fact that it also declines to examine many other cases doesn’t really change that.

Sure, and controversial laws were submitted for constitutional review everywhere around the world (where there are constitutional courts). And picking judges was always a political thing. Just as picking the top prosecutor. And so on.