Yes, you did account for variations, but the way I read your post I thought you were saying that we should all have our sex chromosomes stated on ID documents, and that we should

start calling people by their sex chromosomes and do away

with the two sex categories, male and female.

No more women, no more men, just xx, xy, xxy and whatever other variations exist. Dating sites can be xy seeking xx, xx seeking xx etc. A driver's license or birth certificate can state your sex chromosomes.

But in terms of sex chromosomes, it's the presence or absence of a Y that is most important - or rather, the presence of the SRY gene that's usually on the Y chromosome. Coz that usually is what determines sex. Someone who is XXY is just as male as someone who is XY. Just as someone who is XO is just as female as someone who is XX, coz of the absence of a Y.

I took your proposal that there should be "No more women, no more men" just people identified by sex chromosomes at face value, and tried to express one of the many reason I think that an unwise approach. Perhaps I misunderstood? If so, apologies.

Also, perhaps I am oversensitive to this topic because I and other members of my family were denied health insurance coverage in the USA because we carry genetic "defects" associated with/causative of a fatal disease, and one family member was fired from their job once the employer was informed by the employer-funded insurance carrier what genetic testing revealed about my family member. As a result, I was involved in the push for legislation that would make discrimination based on genetic information illegal in the US. This finally led to the US passing landmark federal legislation in 2008:

The Genetic Information Nondiscrimination Act (GINA) of 2008 protects Americans from discrimination based on their genetic information in both health insurance (Title I) and employment (Title II). Title I amends the Employee Retirement Income Security Act of 1974 (ERISA), the Public Health Service Act (PHSA), and the Internal Revenue Code (IRC), through the Health Insurance Portability and Accountability Act of 1996 (HIPAA), as well as the Social Security Act, to prohibit health insurers from engaging in genetic discrimination. Title II of GINA is implemented by the Equal Employment Opportunity Commission (EEOC) and prevents employers from using genetic information in employment decisions and prevents employers from requesting and requiring genetic information from employees or those applying for jobs.

https://www.genome.gov/about-genomics/policy-issues/Genetic-Discrimination