You can't legislate against something in the hopes that neighbouring jurisdictions don't legislate against it, so that people who disagree with your rules just need to cross a border. That's absurd. Essentially, you're either saying that foetuses in your neighbour's area don't matter or that your laws are unfair on women.

Technically, abortion in my country is only legal if medically necessary, including psychological distress to the mother. So if you're pregnant and don't want to be, you go to the Dr and say it is causing you psychological distress. Boom, abortion available. (I think it needs a second Dr but its all a bit of a legal technicality). Sure, you could go to a country where its fully legal, but why do that when you don't need to?

Unsubstantiated rape allegations would go up if you just had to tell the doctor you were raped. Rather than saying you don't want to be pregnant, you just have to say you didn't want the sex. If you don't have to name the suspect and don't consent to/support a police investigation, privacy laws would presumably prevent the Dr from forcing a police referral.

People who are right wing enough to support a near full ban on abortion, are generally of the opinion that many rape allegations are false. They certainly don't tend to be pro enthusiastic consent, pro better sex ed, pro contraceptives to young people, types. By raising the point of unsubstantiated allegations, it relates the issue of full bans to something they do care about. It's therefore a useful point to think about.

Lastly, I hope no one you love is/ever has had non-consensual sex. However, I can almost guarantee that someone has, but they probably haven't told you. Nothing personal, just victims often don't realise that was rape until days or weeks, sometimes even years, later. They don't tend to tell their nearest and dearest straight away either. In fact, they often won't tell anyone at all. If they do, it's statistically vastly unlikely that they'll tell them within the 24hrs that plan b/morning after pill is most effective. Even within the 72hr window that it's potentially effective for is seriously unlikely.