It would be important to use inclusive language when you want to make clear to whom the language applies. Especially in medicine where people won't fall neatly into the man/woman binary.
If you take each population (cis/trans, biological male/female) separately, there are 8 combinations of people for which we need terms (4 groups of 2 populations, 4 groups of 3 populations). The situation gets more complicated when you add in the fact that trans people may or may not have had gender affirming surgery.
The group for "birthing persons" includes biological females (cis women, pre-surgical trans men) as well as a handful of post-surgical trans women.
as an aside, I personally don't like the term "birthing person" because it reduces the person to some biological function they may or may not want to participate in, and I would prefer the term be "person with uterus" instead.