The Messenger of Allah, Muhammad, married Zainab, the daughter of one of his father's sisters, that is, she was his first cousin. Can it truly be surprising, then, that Allah chose not to prohibit marriage to cousins?
Muslims regard Muhammad as a "good example" to follow. Muhammad married his first cousin, Zainab. Neither Muhammad nor Allah ever condemned the marriage of cousins, with the potential for severe & horrible genetic defects in children.
The video below discusses the prevalence of first-cousin marriages within the United Kingdom's Pakistani community, and the likelihood of genetic disorders among children of such marriages:
A brief digression: We note that Quran 4:23 is speaking directly TO MEN ONLY, and lacks a counterpart verse speaking to women. This is just one of many Quranic verses that speaks only to men. Why is Allah so shy about speaking to women?
With regards to this plea, since Muhammad died Allah refuses to speak to any human.