There are roughly 44-46 speech sounds in the English language. However, we just have 26 letters which denote some of those 44-46 sounds. Why is that? Why we don't represent each of those 44-46 sounds by different written symbols?
Because writing is an invented technology, that isn't subject to the natural processes of language change.
This has various consequences:
Writing needs to be good enough for native speakers to communicate. It doesn't have to represent the language perfectly, and there is little pressure to make it easiar or more convenient for learners and foreigners.
Altering a writing system tends to have costs, both material (the cost of changing printing technology, and possibly reprinting materials that no longer conform) and in human terms (old texts become harder to read, and people - especially older people - find it hard to learn new ways of doing what they've done all their lives)
So writing systems tend to be conservative, not just in failing to reflect changes in the language, but also in hanging onto features simply because that's how they've always been done. English orthography has been shaped by both of these: to some degree, English spelling represents the phonetics of four hundred years ago; but much of its spelling is retained for historical reasons.
Writing systems do change sometimes, often for political reasons; but the reasons must be strong enough to overcome the inherent cost. Proposed changes often fail to be adopted (Some of Noah Webster's changes to American spelling were adopted, but not all). There have been schemes proposed for changing how English is written (one of the most famous was the Shavian alphabet) but none of them - apart from a modest selection of Webster's reforms - has ever been adopted widely. The Journal of the International Phonetic Association, used to print articles (in English or any other language) in IPA, but as far as I know nobody else has adopted that convention for English.
The situation in English is somewhat special, since spelling was first determined over a millenium ago for a different language, Old English. There have been changes in spelling over the years, but changes in pronunciation outstrip changes in spelling. The situation in Tibetan is similar, in that Tibetan was first written almost a millenium ago when it was pronounced very differently. The spelling difference night/knight reflects an earlier pronunciation difference. Further complicating the matter is the introduction of other spelling traditions from French, Latin and Greek.
In terms of the robustly, undeniably distinctive phonemes of Modern English which lead to the problem that 26 letters are inadequate, we have [ʃ tʃ] and a set of vowel distinctions. Some "technical" phonemes are marginal, for example [ŋ] as distinct from [ŋg]; the difference [θ,ð] is mostly predictable when you take into consider the origin of the word (Greek vs. Germanic; word class i.e. grammatical determiner versus lexical root (that, think); causative verb vs. root noun (bathe, bath). The biggest disparity between letters and phonemes in English is one of the two biggest in all languages, the indication of vowel length. Vowel length was a property of Latin, whose writing system we adopted, but even they (the Romans) did not indicate the difference between a long versus short vowel. Languages split in terms of whether they notate vowel length with a diacritic, versus vowel doubling (versus just ignoring length entirely). Also note that linguists split in terms of whether they think of long vowels as being completely separate phonemes, vs. simple "vowels", optionally combined with a phoneme of length.
Changes to spelling conventions for a language with an extensive literary tradition can be socially very disruptive, so if it's not broken, don't fix it. It is admittedly close to broken. However, ordinary people are generally not enamored of fancy letters like [θ ŋ ʃ ʒ ɪ], and in most languages especially those only now developing writing systems, the preference is to avoid special letters in favor of sequences (thus Shona, Taa and Somali spelling reforms eliminated the mass of transcriptional minutia in favor of di- and tri-graphs). It is thus natural that we would be limited to at most 26 letters.