About [ɐ] - what would you say is the first vowel in German aber? The word is usually transcribed as [a:bɐ], but that [a] is probably a convention as well - it's not identical to mainstream English or even Italian /a/. I'd say it's in between [a] and [ɑ]. Northern German as [a] and South Eastern German has [ɑ], both of which are different from the vowel in Standard German.
I agree. I think the German vowel in aber is open, unlike the not-fully-open [ɐ] of STRUT, and is backer than cardinal 4 [a] but fronter than cardinal 5 [ɑ]: in fact, just about halfway between cardinal 4 [a] and cardinal 5 [ɑ].
Here is Mangold’s vowel chart for the oral monophthongs of Standard German (Dudenaussprachewörterbuch6, p. 37).
Some people want the IPA to approve the use of small-cap [A] for this quality. I do not favour this proposal, because no language as far as I am aware distinguishes three fully open unrounded vowels, [a] vs. [A] vs. [ɑ]. Just as the symbol [t] has to represent sounds that may be aspirated or unaspirated, dental or alveolar, according to the language, so we must demand flexibility in vowel symbols such as [a].
If it is essential to symbolize the central quality explicitly, then we have diacritics available: [ä] or [ɐ̞] or [ɑ̈]. But it’s better to state such details once and for all in the transcriptional conventions, not repeatedly in a transcribed text.