The right of the people to be secure in their persons, houses, papers, and effects, against unreasonable searches and seizures, shall not be violated, and no warrants shall issue, but upon probable cause, supported by oath or affirmation, and particularly describing the place to be searched, and the persons or things to be seized.
In order to make all abortions legal because it is a “private matter”, you have to assume, or assert, that no crime can be committed in the commission of an abortion. Otherwise, people selling drugs behind closed doors have a “right to privacy”, as do people running guns, operating illegal casinos, trafficking in humans, embezzling from their employers, etc. The list is endless and can be made to compass substantially all the crimes on the books.
If a pregnant woman goes to a known abortionist, then there exists “probable cause” to assume a crime is about to be committed, if it is illegal to murder fetuses. There is probable cause a crime HAS been committed, if there exist “medical remains”–fetal remains–indicating an abortion has taken place.
Thus, if we accept Roe v. Wade on its face, the same legal logic could be used to affirm ANY crime the SCOTUS wanted to support, if I am understanding this correctly. The bookie taking illegal bets could claim that the law has no business interfering in his private business, and the Supreme Court could concur, thus making all forms of gambling impossible for local jurisdictions to criminalize.
In order for Roe v. Wade to make sense, it has to be ASSUMED that not only is killing a fetus not a crime, but that no legislature of any State has the right to claim it to be so, now or at any time in the future. It has to make an enduring and categorical definition of human life without any possibility of rebuttal or change. This is an assertion without any basis whatsoever in philosophical reasoning or legal precedent. It is the sort of activity Jefferson specifically feared they would start to engage in, and thus ruin the Republic.
It is utterly corrupt intellectually, at the least, and certainly legally. Laws are to be made by legislatures, and are to be mutable based on changing views about a variety of things.