Note also that ~hon changing to ~bon/~ppon is a general feature of Japanese compound words, it's nothing to do with counters specifically.
There is sometimes variation where a person needs to learn which each number for which thing uses which system. For example, with people, a common way of counting is "hitori", "futari" (your irregular cases), and then "san nin", "yo nin", ... (your regular cases). It's not always that way; but the flexibility exists and that is quite different from Chinese.
The sound change -hon to -ppon and similar sound changes are not actually regular in Japanese -- there's not a clear phonological rule for them. Although counters don't generally vary in pronunciation for each count of the counter, many of the common ones do; and these variations must be learned per number, per counter.
The earlier commenter spoke to characteristics of Japanese that might seem unique to a student. Counters certainly are shared with Chinese; but these other things -- the variation in the numbers and the variation in the counter, itself -- are not.
wiki: https://ja.wikipedia.org/wiki/%E9%80%A3%E6%BF%81
As for whether it's unique, wiki suggests that Korean has something similar but I wouldn't know.
My earlier comment did discuss Korean, by the way.
There is a loose rule for compound word contractions (adding tenten to the first letter of the second word), e.g. "sakura" gains a tenten in "senbonzakura". However, as you said, this is not universally the case. For example, "ehon" (lit. drawing book) is simply "e" (drawing) + "hon" (book), not "ebon".
Consider the examples offered: ..."hitori, futari" for people, or "ippon, nihon" for long objects.... The "number part" varies considerably: one and two are "hito-" and "futa-" in the first case and "i-" and "ni-" in the second. In the second example, the counter is "-ppon", with a plosive stop; in the second, it's "-hon" with an affricate. The combination of varying number pronunciations and the
Japanese shares many, many grammatical features with Korean, including much of the politeness grammar system; however, when I looked over a Korean grammar linguistics book recently, I wasn't able to find anything to indicate that counting was as complicated as this.