What a mess it will be if they overturn it, or modify it so that it's de facto overturned. This will be another case of conservative old people legislating their morality on progressive young people.
According to a Pew 2021 survey, people 30 and under are 67% in favor of abortion being legal in all or most cases, compare to 31% against and when you break it down to women only it's even a slightly bigger gap. Only older people are close to being evenly split on this issue.
So yeah, states with GOP-controlled governments will be able to ban abortions and their constituents will celebrate and be overjoyed. But Democrat-run states will allow abortion, and I predict there will be a significant exodus of young people fleeing their conservative home states for the blue states. In the near and mid-term, this will just polarize politics more because political districts will become even more homogenous. But in the long term, the conservative states will become very low population, and the GOP will have a firm control on the senate while perennially losing the House and the Presidency. So, a permanent federal legislative standstill but an overall weakened GOP. Bleh.
People flee theocratic states. There's a reason women are forbidden to leave Saudi Arabia without a man's permission.