In my lifetime, abortions were commonly performed with a clothes hanger on the kitchen table, or in the garage

And it's far less likely someone will do one of these sorts of things than go to a doctor who allows you to pay to have it done. People will always do it, it's that the number will go down by significant amounts. I don't doubt that people will do stupid things, as you describe. I've seen people cut their fingers open and stick magnets in them because they thought it was cool, or people who today eat and get so fat they can't walk intentionally. Using a hanger to perform an abortion isn't that extreme, really. The problem is that it is potentially deadly, and is very dangerous. People can, and will, die trying it, and that will prevent many people from trying it when they would have gotten an abortion.

This is not something you can stop.

I don't want to stop them.

Now go ahead and tell me what type of state-imposed punishment is appropriate for such a person.

I just said there isn't such a punishment that is appropriate. Where did you read me as making such an argument? The state punishment should be revoking the license of doctors who perform abortions. No more, no less. And I don't even think that should happen, people should be free to do what they damn well want to if they aren't substantially/we can know that they harming society by doing so.

I do not think government should enforce law on the basis that being "human" grants you rights to life, liberty, and so on. I think those things should exist because they are beneficial and necessary for a healthy society. Killing babies doesn't really harm much, outside of the point at which you are showing you have no empathy for them, and an "inside" baby isn't such a being. I don't know if you mistook this argument as one "for" abortion, but it isn't one.