It's dumb because there are two types of hyper/hypo-gonadism. "Primary" hypergonadism is where you have way more of the hormone in your blood stream. You're advocating testing for only "primary hypergonadism" in women.

Secondary hypergonadism is where someone has a normal concentration of the hormone in their blood, but they have an unusual abundance of hormone receptors.

The effects are the same, but currently we can only measure secondary hypergonadism during an autopsy/dissection.