Regulation is another red herring. People who are against abortion are not interested in regulating doctors, they are for 100% outright bans on any form of the procedure.
We know that's false though, just through polling. The majority of Americans support abortion with restrictions. Very few people support non-medically necessary abortions at 39 weeks for instance. So to prevent that, you need regulations to draw the line somewhere, wherever that line is being up for debate.