Hi, I’m a casual linguistics nerd (no degrees), speaking Philippine English with heavy American influence.
My accent of English has pre-nasal /æ/ raising and I’ve caught myself raising it in other places like before /g/.
When I look at English language learning videos (out of curiosity) I have not found anyone mention /æ/ raising in them.
Why is this case?
This is just a conjecture, I’m not informed enough on English to know what’s up, but.
I think the pronunciation of a language, as taught to non-native speakers, is usually biased towards more conservative variants; specially when there’s a lot of variation going on. In this case towards realising /æ/ as [æ] instead of [ɛə], [ej], and others.
For reference, I’ve seen something similar popping up with German unstressed -er (eg. kleiner, Kinder, unser, etc.); most native speakers would realise it as [ɐ], and yet when I learned it it was “supposed” to be [əɐ̯].
It’s certainly true that many British English dictionaries are quite out of date with their pronunciations, with many still using the RP accent which you almost never hear in Britain nowadays.
There are some who are updating things, like Geoff Lindsey and his SSB CUBE (CUrrent British English) dictionary (although they haven’t updated to have https, for some reason).