It's far harder to move citizens between countries and would basically be impossible on a large scales like this. Currently people are free to travel between states but who knows in 5-10 years? They may make women take pregnancy tests at the borders of states.
Somewhat. They're free to travel, now, as you say, but Missouri now has the crime of "conspiracy to commit abortion" to cover you getting in your car to drive out of state, or booking a flight out of state...