Why is the use of 本人 appropriate in the contexts below
In all your cases, the writers are deliberately trying to sound formal.

In the first piece of article, the writer is asking to rent a house. It is quite common in China for this kind of article to use "formal" language.

And using formal languages can make people sound "serious". On "知乎", people use this kind of language to show that they are seriously seeking for an answer to their questions, but not just randomly poking around. For the colloquial "求計算機大神導致", "知乎" is an internet Q/A service, so it is quite common for this kind colloquial phrases to appear. (It might be kind of scary for an article made up of purely formal language to appear here.)

"本人" does not usually appear in (one-on-one) conversations. So it may be also rare in (one-on-one) text chat. But if one is sending a message to many people, he usually changes into a somewhat "formal" language, if he is indeed serious about the message.

In all the quotes in your question, there would not be any problem replacing "本人" with "我". The seriousness of the text is not carried by "本人" only, so there would not be too much difference.