No, this is a deep take, not a shallow one, but you may have missed the point.
The real issue here is whether it is wise to permit government access to private knowledge about our bodies. Everyone has an opinion here, which is why it’s a political issue, but my moral rejection of abortion as flat out equivalent to murder has nothing to do with the fact that I don’t believe the government should be given private medical data to prosecute such crimes.
Something can be morally objectionable and this doesn’t mean we should grant government powers specifically forbidden (such as unlawful search and seizure) to it just because we object to feticide.
Feticide is bad. Giving government the powers needed to prosecute feticide has a lot of downsides.