So first off, a language is not the same thing as a writing system. While it's true that the modern Hawaiian writing system is based off of the English alphabet, the Hawaiian language, however, has no special affinity with English other than language contact relatively recently in the history of each language. More generally, there is no special connection between languages that share a writing system.

Also, the sounds Hawaiian alphabet represents are not the same as English. For instance, the ʻokina, which many English speakers gloss over as unimportant punctuation, is actually a consonant--called a glottal stop, and omitting it, either in writing or in speech, can completely change the meaning of a word. For instance, Lānaʻi is the name of one of the main Hawaiian islands, whereas lānai means 'veranda' or 'porch'. Also, some letters do not represent equivalent sounds. English w typically represents a labiovelar approximant, while in Hawaiian it represents a labiodental approximant.

Simply put, the people of the Hawaiian Kingdom had no reason to adopt English at the time. Hawaiian was the language of everyone on the islands, and everything they needed to do could be done in Hawaiian, from day-to-day conversations, to newspapers, to two constitutions, one in 1839, and a second in 1852.

The adoption of English in Hawaii was a slow process, resulting from various factors, including conversion from traditional Hawaiian religion to Christianity, the overthrow of the Hawaiian Kingdom, the shift in land-ownership and economic power towards Euro-Americans, the massive decline in the native Hawaiian population due to epidemic disease, and the introduction of many non-Hawaiians on the plantations.