Disclaimer: I'm a Japanese native learning Chinese.
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.
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".
The latter case is perhaps the easiest, since "slippery" is an adjective derived from the verb "slip", still in use. (The word "glitter" is also derived from a verb, but this verb is no longer used.) Generally, words that are onomatopoeia don't have an etymology like that; if they did, then the sound would not be the result of trying to create the impression of something. For example, the "-y" in "slippery" is there because it's an adjective. The extent of onomatopoeia in Japanese is indeed quite different from English (and Chinese).
I'm trying to learn the language, but man it's difficult.
I get there's a subtle difference but it's not that far off. We also say "I have 6 meters of rope". "meters" is the counting unit, which is the same concept as all the Japanese counting units.
As for the onomatopoeias, at some point you get used to them and they feel like they fit and you can start to pick them up without having them explained. Even the ones that don't seem like the make a sound, start to make a sound, at least in my mind once I've internalized it.
Not the same but in some sense similar, dogs don't say "bark" but with enough repetition many people perceive "bark" instead of the actual sound the small dog is making.
There's nothing context-wise that suggests one is supposed to suffix "hon/pon" (lit. "Book") when you're counting carrots, while tomatoes are counted with "hitotsu, futatsu". The rule for flat things is to suffix "mai", but while postcards are "ichimai, nimai", magazines are "hitotsu, futatsu" and pamphlets are "isatsu, nisatsu". Having to remember these seemingly arbitrary rules as a Japanese learner is often considered a bewildering experience.
IIRC 冊 = bindings (very similar to the concept of pairs of socks, we have bindings of paper). So you count "sheets of paper" (枚)and "bindings of books" (冊).
All I'm saying is there are lots of place in English were without a counting unit it's often awkward or ungrammatical. I agree it takes take some getting used to all the counters though and even Japanese have trouble with it as there's a game you play where you call out a thing and the next per says that thing +1 +the counter.
Example player 1: "Apple", Player 2 "apple ik-ko. banana", Player 3 "banana nip-pon. car", Player 4 "car yon dai. house", Player 5: "House go-ken" Player 5 might have just gotten that wrong and then everyone would laugh.
Edit: and there are the fun cases where it's not always on or kun: ichinichi, futsuka... or other fun exceptions.
Of course, it depends what you use Japanese for.
The "desu" isn't strictly necessary. You can just say "oishikatta".
With that said, Japanese does have a bunch of curious features, like different words for ordinal numbers depending on what you're counting (e.g. "one, two" can be translated to "hitori, futari" for people, or "ippon, nihon" for long objects, or "ippiki, nihiki" for small animals, etc), a plethora of onomatopoeias even for things that don't actually make any sounds - notoriously, "pika" (as in pikachu) is word for the "sound" of sparkling, politeness conjugations (e.g. "da" vs "desu" vs " de gozaimasu"), and many other things.