The reason is because the combination 'ch' used for transliteration is usually pronounced 'k': the only English word I can think of where 'ch' is pronounced in the Greek way is 'loch', which isn't even a Greek word. If we used the Greek pronunciation of words such as 'chronometer' or 'synchronous' we would sound very odd, the same applies to 'chi'. I studied Ancient Greek at school, and we used English, not Greek, names for all the letters of the alphabet ('alfa' , 'beeta' etc., not just chi), this is perfectly normal and 'well-educated'. Another example is 'ph', which we pronounce as 'f', rather than an aspirated 'p' as the Greeks would have pronounced the letter phi, so we pronounce the letter's name as 'fie' rather than 'pee': maybe the answer is more obvious in this case.

In classical Greek, character χ represented the sound "kh" (the sound of "k" followed by breathing noise). I think it was Romans who transliterated the Greek character as "ch" but the idea is the same because ancient Romans pronounced letter "c" as "k". That's how we have spellings like "technique", which is based on the Greek word τϵχνη (techne), "character", "mechanical", etc. So, the Greek name χι of letter χ is transliterated to "chi" and pronounced "kai".