@gronkle I really was just gonna let this argument go on, but replacing otou-san with dad is absolutely NOT equivalent with replacing onigiri with jelly donuts.
Where otou-san and dad generally mean the same thing, especially with this context in which we know how Yaginuma speaks, the modern time period, and it's not like they've left every instance of 'mother' untranslated (pg 4). We know that Yaginuma is close with his family, hence 'dad' would be a sufficient equivalent. If, say, he were formal with them and he used "otou-sama", "father" would be a sufficient equivalent. Regarding your examples, I'd argue that "dada" and "daddy" would all probably fit into "tou-chan" or "papa" (though I've never heard dada outside of a toddler's mouth). "Pa", "pops", and "pappy" would probably fit into "oyaji" or "jiji", maybe "tou-chan" if they're being affectionate. "Father" and "dad" would fit into "Otou-sama/san" depending on how their relationship is, and I've literally never heard "pater" being used outside of a prefix or latin.
The only time I'd say that family terms shouldn't be translated would be with the -ue suffix (chichi/haha/ani/ane), because I don't think there's a real equivalent in the English language, though I've seen some people make do with adding terms of respect before the term or just making the sentence really formal (Lord brother, etc.). Seeing as how chichi-ue and the like aren't often used in modern times, besides extremely formally or maybe in some historical dramas, I think that's a fine translation choice.
I think it's also important to note that I believe that translation should be localization instead of being a literal translation. I feel like those that prefer literal translations always say that they want to hear the author's voice in the work, or that it's to preserve the Japanese spirit of the work, but by translating it in any way, the story has become the translator's. If you want to not lose the nuance of things in Japanese, then I'd have to ask you to read the work in Japanese.
tldr: there's lots of ways to show nuance in the English language, though messy a language it may be.