It makes sense but it is a false framing. The whole point of female and male is to distinguish the two reproductive roles in sexually reproducing species, whether those are hermaphroditic or gonochoric. The sex binary is based on anisogamy, that is, two classes of gamete being of unequal size.
All the "dimensions" you mention - hormones, chromosomes, etc. - are downstream of this, and they vary across species (e.g. some don't use hormonal signalling for reproduction, but neuropeptides). While there are variations, including those in sex development that may lead to a disordered system, it doesn't logically follow that sex itself is a spectrum.
To take one of your examples: a hirsute woman with elevated testosterone due to PCOS is female, and having this condition doesn't make her less so. Indeed, this is a condition that only affects people who are female, tied to ovarian function. Her condition can be described perfectly well without pretending that her sex lies on some sort of ill-defined spectrum.
Your comment about "drawing an arbitrary line" doesn't really fit with how biologists see this either, as it's not arbitrary at all but is based on understanding the mechanisms of reproductive function and development. And not based on gathering and arbitrarily categorising data without reference to the underlying system. The mechanistic insight is important.
Going way back upthread, this was originally about fairness in sport, male physiological advantage, and the other commenter getting surprisingly cross at me describing males as male, as he seemed to think there are medical interventions that can be performed on humans that convert males to female, which is not the case. Then you commented stating that sex is a spectrum. This is typically introduced into an argument to try to bolster the claim that it is possible for humans to change sex, the idea being to redefine sex as a cluster of characteristics to be considered separately to reproductive function, and then argue that because things like breast size (through a male taking exogenous oestrogen) and genital morphology (such as surgically inverting a penis to make a hole, and lining the entry point with scrotal tissue) can be changed, this constitutes a change in sex (e.g. a male, by this redefinition, supposedly becoming more female).
So that leads into another issue of why this "sex is a spectrum" idea has been introduced to the world at large. It is not to gain greater understanding of reproductive system, sex development and evolutionary questions regarding sexual reproduction. We can see even from this back and forth between the two of us how it only has rhetorical use, with my requests for precise detail on how this model might work in practice remaining unanswered.
Thanks for the discussion, interested to hear your thoughts on this.