The equivalence is problematic because the illegality of drugs spurs people to try harder to get them due to the taboo factor. I doubt it being forbidden would make people want abortions more.
Is there any evidence that prohibition increases demand for recreational drugs? I frequently hear this argument, but no one seems able to show that this is the case.
Well, it doesn't seem to REDUCE demand.
Though, it would be interesting whether there were ever was a War on Abortion. When it was illegal, Was there much of a demand for them in the first place? Were the police able to stop/prevent most of them? Was there aggressive public policies against them? (PR campaigns, public crack downs, mandatory minimums, specific civilian and paramilitary/police task forces that targeted abortion), and if there were "bad guys", was there a "pussy mob"?
Basically, was abortion in 1953 like drugs in 2003?