I don’t thing abortion was ever POPULAR, so much as it remains an ugly fact of life throughout the world. Only destigmatization of single parenthood, poverty reduction, vastly improved antenatal healthcare access, and medical advancements render it obsolete.
Think of it like alcohol prohibition, or prohibiting cannabis. You want to stop people using the practice, not move it out of sight. So you need to address the causes of use, not just ban the consumption.
I’m a libertarian. A better solution to banning any product is to create the circumstances where people don’t ever “need” let alone “want” the product. Sometimes that means, you just need a mass market alternative.
What “products” can make abortion seem like an unnecessary solution to a nonexistent problem? Condoms. The Pill. The Morning After Pill. Humane surrogacy and adoption processes. Guaranteed healthcare support for expectant mums and their babies. Not expecting women to make a binary choice between career and motherhood.
It’s not rocket science.
If it does nothing else, having jurisdictions which choose to criminalize abortion will be a safeguard against promotion. Even a few states which do this is a powerful bulwark against the forces of darkness - Nationwide.