I'm not entirely sure about how the pronunciations developed. I know that in modern Japanese there are only certain ways syllables can change their sound. Japan uses a syllabary rather than an alphabet, so for example they can only say the sounds bu and ra, but never "bra" because they don't have a standalone "b". Their syllables get modified in predictable ways, like ka can change to ga, going from a voiceless to voiced velar stop. In much the same way, the ho syllable can become po.

I don't know much about the history of when nippon became nihon, but the article you linked has a short section on it

Japanese 日 and 本 were historically pronounced niti and pon, respectively. In compounds, however, final voiceless stops (i.e. p, t, k) of the first word were unreleased in Middle Chinese, and the pronunciation of 日本 was thus Nippon or Jippon (with the adjacent consonants assimilating).

Historical sound change in Japanese has led to the modern pronunciations of the individual characters as nichi and hon. The pronunciation Nihon originated, possibly in the Kantō region, as a reintroduction of this independent pronunciation of 本 into the compound. This must have taken place during the Edo period, after another sound change occurred which would have resulted in this form becoming Niwon and later Nion.