The author's arguments are based on the incorrect notion that there is a "pro-choice majority". That was true twenty years ago, but not today. Polls show Americans are evenly split. In blue states there are pro-choice majorities, and red states they are pro-life. So putting the issue on state ballots wouldn't change the overall political picture. It would mean abortion would be illegal in many states, severly restricted in others, and unrestiction in the rest. The law would conform to what the people and their legislators decide. Works for me.
I'd like to see the wording of the polls you cite.
There is a current FR poll right now in which 42% of registered Freepers are in favor of a constitutional ban on all abortion and 40% are in favor of a ban "with some exceptions". That's very telling considering where Freepers are positioned on the spectrum.
My guess on where the public is at large would be something like:
-20% endorse abortion at all times, right up to the morning before labor begins
-25% oppose abortion at all times, even if it's a raped 12-year old carrying an anencephalic baby
-55% oppose abortions of convenience and abortions performed after fetal survival is possible, but do not object to very early term abortions and those performed after rape/incest or when the child will be born cataclysmically deformed.
That should give a clue as to where I think state laws would go in a post-Roe era.