I do not think that the prostate analogy is fitting. The risk of prostate cancer increases with age - CDC - Prostate Cancer Risk by Age. Therefore, there is a non-arbitrary reason to schedule exams starting at a certain age. Likewise, amniocentesis is recommended for pregnant women after a certain age for the same non-arbitrary reason: the risks increase with age. Colorectal cancer, same story - risk increases with age: CDC - Colorectal Cancer Risk by Age

In the case of sexual activity, the relevant part is whether a woman is sexually active, which is not determined by her age.