I would expect most of these sounds to follow similar rules. Sometimes there might be something like clicks, but in general similar sounds will be used. And certain styles will probably cluster as well.
In the end you have handful of options and thousands of languages. So some must end up being similar.
Why not? Many unrelated languages steer towards the open syllable rule. It's basically the only similarity between Japanese and African languages. Open syllables without complex consonant clusters are easier to pronounce.
Say, Proto-Slavic phonetics mostly allowed only open syllables, although its ancestor and descendants allow more complex clusters. For example, Proto-Indoeuropean domos "house" became Proto-Slavic domu, and mater "mother" became mati.
Let's list some Proto-Slavic words: noga "foot", ronka "hand", nosu "nose", oko "eye", podushiwa "foot sole", noguti "nail" etc.
You can cherrypick many languages like that (Finnish, Maori, Basque, even French to some extent)
It would be much more surprising if they found 2 unrelated languages and they both had same complex clusters a la Georgian (mtsvrtneli "trainer").
As to why it felt off: identical patterns across as-yet unconnected distributions is usually an early indicator of undiscovered relation.
Your suggestion of language steering toward open syllables may well be that relationship.