Which means that any state could then prohibit abortion at least in their jurisdiction - precisely because abortion ceases to have said constitutional protection. IIRC some states have laws that would make it illegal with the usual exceptions in such an event.But look at what a reversal means. It does not mean that abortion will be prohibited in the United States. Rather, it means that abortion protections do not formally exist as part of the fourth amendment nor the fourteenth. That in itself will mean little for the legality of abortion anywhere in the United States.
Sure, it would still be widely available - just cross state lines - but the fact remains that the option remains open to ban it in a particular place. Certainly many states will continue to allow it, though, and Americans on either side of the issue, by and large, aren't interested in placing the issue under Federal authority in such a case.
Either way, it'll be one of the issues which, owing to the sheer size and diversity of this country, will not die for another few decades, at least.