'I can't see the court ruling that abortion be exclusively a states right. What part of the Constitution would allow them to rule that way? So the question is, could this decision actually lead to outlawing abortions on a national level?"
That was the situation pre-Roe. 4 States fully legalized abortion and about around 15 others "liberalized" their laws to allow women to have access to abortion.
commons.wikimedia.org
In theory anyway, Fillibuster still applies to social legislation, so while it may constitutionally be possible to either nationally codify Roe or ban abortion entirely even for rape incest and health of the woman, I don't see that happening .... without eliminating the fillibuster. And imo that will happen as a result of Alitos opinion ... one way or the other.