And look at how Wade v Roe turned out. And Privacy isn't explicitly mentioned once in the Constitution, except indirectly via the 10th, meaning that at the end of the day, without the will to fight and prevent encroachment, it's as fair game as anything else.
> Meaning "state of freedom from intrusion or interference" is from 1814.
So instead they used phrases such as "secure in their persons, houses, papers, and effects" in the 4th amendment for the same general meaning.
Edit to make the specific point explicit: A right to "privacy" does exist in the US Constitution, however this right can be broached with a warrant and a "reasonable" search and seizure. The right, in and of itself, does not protect against any particular laws, including laws against abortion.