That depends on how you construe it.
Abortion isn't a national issue, it's a state issue. Which means that people living in Georgia or Texas don't need to bend the knee to liberals in New York or San Francisco.
That also means that the only "broad popular support" that matters is the broad popular support in the given state in question.
Which goes back to your original point - abortion in the south (hopefully) will be gone - if thats what the people of southern states want.
And if it goes elsewhere, that means the people of those other states also want it gone there, too. And it should be left to those people to decide.