I've found several articles that promised to explain why they became popular, and none of them actually answer the question. "The first pointy bra was the chansonette in the 1940s" and "worn by several leading ladies", etc. Okay cool, but why? At some point some underwear designer said "we want breasts to look like this now". What for?
I've heard it said that the shape was meant to suggest a torpedo, a well known image in post-war America. But some actual documented evidence would be great.
I've previously written on this topic! You can read my answer here: Why were women's, ah, undies noticeably more pointy in the 1940s-60s? Fashion? Body shape?