The reason Danny doesn’t work, and Jane does, is that Danny Castellano’s character is about being Catholic. Jane simply is Catholic. This is also true of her ethnicity: Her character is not about being Latina, she simply is.
“Jane the Virgin” does not understand itself to be “the Catholic show” any more than it understands itself to be “the Latino show,” but in both cases, the show is under immense pressure to be both representative and commercially successful in order to pave the way for future stories. As a result, the show is subject to unreasonably high standards. “Jane the Virgin” cannot represent all Catholic stories, or all Latino stories, no matter how astute the writing. Rather, its specificity to one family doing its best to grow in love is precisely what makes it valuable—not just to Catholic viewers but to everyone.