Abortion's a contentious issue because there are passionate people on both sides and a relatively even split in public opinion. If it weren't handled through the court, "vote so we can preserve/overturn Roe v Wade" would just become "vote so Congress can pass/repeal an abortion ban."
I think the things that are specific SCOTUS problems are issues where there's a clear majority on one side, and the court is ruling against it not to preserve a broadly-understood restriction on government power or to protect a mistreated minority, but using some particularly abstruse reasoning to reach an ideological/partisan conclusion (eg Citizens United, Janus).
In that vein, what concerns me most about Kavanaugh is his weird ideas about bureaucratic rule-making being unconstitutional, which could be applied to wreck whichever agencies the court doesn't like politically.
