Another point against using the phrase "pregnant people" instead of "pregnant women" is that it leaves no way to talk about women who aren't pregnant. "Non-pregnant people" includes every man and every prepubescent child.
That is _your_ definition, and it is very debatable.
Nature disagrees with you. There are many animals out there that can change sex. Sex, gender, etc etc don't have a perfect universal definition because nature doesn't work that way. The scientific literature is trying to capture the observed variety we see in humans and it will continue to evolve as our understanding evolves.
This whole line of argument reminds me of the history of pi and the governments that tried to legislate it to fixed values. Just because you want things to be simple doesn't mean that reality backs you up.