Earlier quoted context omitted.
I don't think it's as complicated as you're describing. There are just two systems; the regular case with regular numbers, and irregular cases using hito/futa/etc. One has to learn which counters use which system, but there are just the two of them. Note also that ~hon changing to ~bon/~ppon is a general feature of Japanese compound words, it's nothing to do with counters specifically.
All the things described are real features of Japanese counting and are real examples drawn from the Japanese language. 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 f…
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".