Perhaps, but IMHO it’s an interpretation to stipulate that some other Constitutional right does not cover abortion. For 50 years, under Roe, the SCOTUS view was exactly that. Now suddenly it isn’t protected, because the ideological tilt of the Court changed. SCOTUS Justices interpret the law according to their ideology but justify their interpretations as somehow more aligned with the Constitution that competing interpretations.
IMHO, the Constitution is general because a) it is old and b) it can’t cover every possible situation. For example, it is used to protect the right to bear arms. I doubt our Founders would have intended ordinary citizens to have assault rifles. Yet, SCOTUS interprets the Constitution to mean just that.
The problem with letting states make these decisions is that once again, poor people suffer because they can’t afford to travel. Plus, some states want to prevent people from leaving the state to get an abortion. IMHO one can't justify a law that prevents people from leaving a state to do things in other states as somehow aligning with “states rights.”