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.
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.