Those were only few examples, there are a lot more people who shouldn't be able to look into information like this like security guards, the police when they are checking your ID etc. With the two new genders it would be easy for everyone who is able to look into your ID tell that you're transgendered. Would you want the cashier knowing about your past when you buy a beer or a cigarettes? Or the lady at the customer service when you are picking up your package? There are so many places that don't need to know about this at all. Even among doctors there is often no need for them to know about your past. For example, dentists have no need to know about it or shrinks(unless you are going there because of your transgenderism).
Even though doctors might have some reasons to know about your birth sex, it doesn't mean that all of them should have access to it without problem. There aren't all that many disease that are chromosome orientated. Not to forget that your doctor will most like know about your transgenderism even without you telling them simply because you need to get your prescription for the hormones from somewhere. These diseases should be rather are anyway.
My main problem with people, even doctors, having access to information like this is that it makes it more vulnerable for misuse. I don't have a problem telling a doctor about my transsexuality but I don't want them to be able to check it from something else just like that. Especially as if doctors have access to them that also means that nurses can get access to it. It's just information that can be misused so easily, so one doesn't want it to be kept anywhere easily available.
Besides, when there is something they can't solve, they usually go through all possibilities anyway. Latest than the patient himself/herself can tell about the birth sex. At least I've never heard of a disease that is based on chromosome that can kill you fast.
EDIT: Almost forgot. What does TSA mean?