The main problem with your position is that it does not comport with the actual colloquial usage of the terms.

Yes, if it were true that "male" always meant "biological male" and "female" always meant "biological female", then having a distinction between man/woman and male/female would capture a lot of the complexity of how people identify vs. how their bodies developed.

Unfortunately, because gender identity and sexually dimorphic development are highly correlated, people have already frequently decided that the terms are interchangeable, or that one is just a broader or more formal term than the other.

For instance, a woman is an adult. What do you say if you want to refer to anyone, adult or child, who has that gender identity? Well, it's ever-so-tempting to use "female", because "female" does not presuppose any particular age.

Furthermore, which term is most pertinent depends deeply on the application. If you are trying to identify someone who has committed a crime, or to check that they are who they say they are, you want to use the term that most likely matches how they present (although if you have a picture, that would be far better...). If you are running a fertility clinic, you need to know about their reproductive biology. In medical contexts, both original morphology and present hormonal composition can be very important.

So I think the strongest claim of this sort that one could sustain is that in certain contexts "male" should be understood as biological male and "female" should be understood as biological female. If it's not clear, one can use "biological" or "developmental" to clarify--and I do agree that having to always use these words unnecessarily impedes discourse and understanding (c.f. "brevity is the soul of wit"). However, in other contexts, this restriction is already relaxed and it seems unnecessarily disruptive to change all our usage to cover an otherwise relatively uncommon case. In particular, I don't think your strongly prescriptivist position is reasonable because of the scale of effort society is required to exert in order to adhere to your ideas. For instance, if a passport says "F" but a child presents as a boy, that's considerably less useful than if the passport says "M"..."B" would work fine also, but the effort required to get to that point is immense.

However, I think the idea can be reasonably entertained and one can have a reasonable discussion about it.