Why do we use /ʌ/ to denote the "u" sound in "cup" and not /ɐ/?

Answer 1

Although the phonetic realization of /ʌ/ is closer to [ɐ] than to [ʌ] in General American and Received Pronunciation, there are still some dialects that pronounce /ʌ/ as [ʌ]. Historically, the vowel in "cup" was pronounced more like [ʌ], and thus the convention has been and continues to be to transcribe it as such even though more widely spoken varieties may not actually pronounce it that way.