Bans also make the activity more physically dangerous. Banning abortions just means women will do them in some unregulated, dangerous back alley. Banning gun sales just means people have to deal with the black market and gangsters to buy them. As much as I hate sports betting, banning it means the gamblers will go to some shady bookie who will break their fingers if they don't pay up.

It does do that, but it doesn't just do that. People will avoid illegal activity just because its illegal, especially if it exposes them to personal physical risk.

Prohibition did reduce alcohol consumption by at least one-third. Didn’t necessarily make it good policy, but it did reduce alcohol consumption and did reduce a lot of the health harms associated with alcohol consumption.

Those in an acute need of an abortion are most often those in dire circumstances: victims of a rape, those who somehow forgot to use protection (e.g. due to being drunk), or, worse, not educated about protection in order to "save their innocence". Most of the general population is affected much more rarely, so an abortion ban hits the most vulnerable more.

With handguns, it's similar: the people most intent on obtaining a handgun are often people who have an intention to use it as an attack weapon: violent criminals, or people planning a violent revenge. They care least about breaking (some more) law, and, if handguns are banned, obtain handguns with a much higher probability than an average law-abiding citizen (police officers are below 1% among general population). So the most vulnerable groups have the least chance to protect themselves with a firearm. (Though, truth be told, a pump-action shotgun is a much better defense tool if you defend your house.)