Well, personally, despite not having any religious factors involved, if there were a definite, credible test that would tell me the exact reason why I turned out to be the way I did, I would really want to get it. I know it wouldn't change anything in my transition.
Well, -perhaps- it would have me get another treatment/more tests in very special cases (for example, if I had an intersex condition that for some reason causes X health problem to happen often or Y organ to often flinch at age Z)... but that wouldn't really be part of my decision.
It's just that I feel much better if I know -why- about everything. I really feel bad about things if I can't understand them as much as I would like to. And even more if it's possible to know. For example, if someone tells me I have to put this recipe's dish on the top grid of the oven, not on the bottom one, I'll get annoyed, even though the most logical answer is "who cares?"
So I understand the OP's feelings. My psychiatrist made me do a karyotype test, too, "just in case", and honestly, I'm happy he did. It doesn't change anything in the world that I am simply a transsexual and don't have a genetic anomaly. But I still feel somewhat relieved to know. Ignorance is annoying, even when which answer it is doesn't have any effect.
Moreover, if I were considering sperm banking (which I am not, but anyway) it would be a very pertinent information to know whether I have a sex chromosome anomaly. Some of them cause infertility, and I'm not sure that would be something the technicians would be able to see (they don't dig as deep as the genetic material, do they?) so they might tell me my sperm is good, and when the time would come to use it, there would be no results, so I would have ended up having no results.
And in the event that the anomaly that I would have would not cause infertility, I would probably not want to bank my sperm anymore. I certainly wouldn't want to risk passing the anomaly on to my children. For whom in the world would the relatively small additional joy of having their own genetic material in their child outset a high risk of that child having a genetic anomaly that might have them go through the same things as themself? Or even worse symptoms...
PS: If that nurse doesn't know that it's possible to have genetic variations of the sex chromosomes, she seriously needs to go back to school...