Exactly, because that argument is so far-fetched and cruel, that it's rarely seen outside of online debates. Having an abortion is still cruel, but there are always ways for people to do shameful things while putting their consciousness aside. It's probably rather easy for most.
I think your argument on the health of the baby (or mother) is more ethical than any "no right to use her body" argument. She was the person who decided to put the fetus in that situation.
To make a comparison, there are people arguing that the fate of prisoners in the German death camps during WWII was not really the Germans' fault because they didn't have enough food to feed themselves, much less war prisoners and other detainees. Which is inching quite close to the abortion arguments, especially if you reduce the victim to subhuman status. Hoping to show that this way of reasoning is misguided.
I don't find the German death camp analogy accurate or compelling; the Germans actively and deliberately herded up the Jews (and others) locked them up. This conscious intervention in the course of a living human being's life rendered responsibiloty onto the German state.
Have you heard of Judith Thompson's "famous violinist" thought experiment? [0] It neatly captures the idea of how a right to life oughtn't extend heavy legal responsibilities onto an individual. At least, most people would say that the main character has the right to say "no" to the situation.
[0] https://ethics.org.au/thought-experiment-the-famous-violinis...