The federal system was established by the Constitution in the first place because the Articles of Confederation made such a mess of governance after the Revolution. The abortion controversy is not going to be solved by a "state's rights" argument.
The opposite is the case. It only makes sense for a state to pass a law when conditions local to that state are at issue. Human bodies and pregnancies are the same in all states, and the issue of individual rights ought to make no difference according to state boundaries. There is no reason why one state should experience a flood of women seeking abortions because a neighboring state has arbitrarily decided to ban them. That became clear when a pregnant Georgian woman died, because she had to travel to North Carolina for medical care, only to find that she had missed her appointment in an overburdened hospital system. My own state of Washington experiences the same thing because of neighboring Idaho.
I'm sorry, but that is such a looney argument. Why should people have to move to a different state on the off-chance that they might need an abortion? It is not as if women actually plan to have abortions. What determines where you live depends on where you can make best use of your abilities to earn a living, not to find a place that resolves all of your political opinions. You seem to fantasize a country in which people are constantly bouncing around like ping pong balls every time they change their minds on some hot button issue.