The vowel in "Tank" sounds more like ɛ to me, yet the IPA spelling for "Tank" (as pronounced in General American English) employs the ash [æ] to represent the vowel. The same for the word "thank" in GAE. Is [æ] appropriate in these cases? Shouldn't this vowel be represented with another IPA symbol?
Keep in mind whether you are you looking at phonetic transcriptions or phonemic ones. I would say that phonemic ones are more widely used (e.g. that's what you'll find in dictionaries) and tank is generally considered to have the phoneme /æ/. Note also that the use of IPA symbols does not follow strict rules, even in phonetic transcriptions. The International Phonetic Association gives guidance on the official meaning of the symbols, but linguists use them in whatever ways they find useful, so there often isn't a single fact of the matter about what transcription of a particular sound is most appropriate.
That said, the phonetic quality of the vowel in tank may differ substantially from IPA [æ] in many American English accents. The vowel in tank tends to be raised; the most common phonemic transcription that I have seen for this phone is actually [eə], although [ɛə] is similar. Different accents have different conditions for raising /æ/ to [eə]; in my accent, this happens before all nasal consonants, but others may differ. Some accents, e.g. in Minnesota, have raising before /g/ as well. I have also heard that some speakers find that original /æ/ before /ŋ/ is realized with a high offglide, becoming something that sounds to them like the vowel in tame (e.g. something like [teıŋk].
Using phonemic transcriptions such as /æŋ/ avoids having to choose between these kinds of alternatives. This can be useful because people often want to talk broadly about English rather than specifically about a particular accent.