Is there is a possibility of English phonology being misanalyzed, with English actually having many consonants and only few vowels, like Cherkess, for example?

It has an odd vowel system with great many glides and di/triphthongs, something common for the surface vowels in consonant heavy langauges, but uncommon otherwise. The vowels don't form a neat, evenly spaced grid like in other languages. Mandarin Chinese is an exception, but it was also recently reanalyzed as only having two phonemic vowels, with all the other vowels being allophones.

The vowels are highly unstable, with vastly different pronunciations in different dialects and over time. This is nevertheless perceived as mere "accent", despite the "same" vowel in different accent sometimes being more different than two different vowels in the same accent, suggesting the vowels are indeed more prosodic than actually phonemic. Meanwhile, Spanish turned /e/ and /o/ into /ie/ and /we/ in the nearly two millenia since Vulgar Latin.

Even native speakers cannot syllabify words easily, unlike most langauges where native speakers perceive the syllables as obvious and unambiguous, while in English even dictionaries may disagree on how to syllabify words. It almost seems as if the consonants were the nucle, instead of the vowels.

The perception of native speakers themselves that consonants are far more important than vowels.

It seems that I sound more native and natural when I concentrate on the consonants and mostly ignore the vowels.

Abkhaz and the extinct Ubykh, two phonemic vowels, those in my opinion seem to have most English-like sounding vowels:
https://www.youtube.com/watch?v=oOAnumDL3sk
https://www.youtube.com/watch?v=vidSM6wfLoU

Two dialects of Cherkess, with likely three vowels:
https://www.youtube.com/watch?v=nvoKewWI_3s
https://www.youtube.com/watch?v=IOlmCCwnWj0

And marshallese with either three or four vowels:
https://www.youtube.com/watch?v=VziOp3PgBDs