If Roe were to be overturned, all that would do is return the question of abortion to the states. At least ten states would continue the practice of rampant abortion (CA, OR, WA, NM, IL, NY, CT, MA, VT, HI). Of the remaining forty states, some would outlaw abortion, some would restrict abortion, a few might continue to allow all abortion, most would allow "Plan B" abortion.
In those states that outlaw abortion or greatly restrict it, Planned Parenthood-type companies will run a kind of underground railroad funneling pregnant women into states that continue to allow abortion, so that the overall number of abortions is unlikely to decrease significantly.
Roe should be overturned because it is bad law, the way Dred Scott and Plessy were bad law. But only useful idiots on the left believe that overturning Roe will turn America into a low-abortion society. For that to happen would require something that the left fears far more than Kavanaugh: a Third Great Awakening and a national return to Christ in particular and Judeo-Christian ethics in general.
Or an amendment to the constitution declaring that life begins at conception. Of course that has about a snow balls chance in hell of ever passing.