Why is /ɪŋk/ used with "ink" words when the actual pronunciation is /ijŋk/?
SOURCES
1) Words correctly coded /iː/ sound for "i"
a) routine /ruːˈtiːn/ https://en.wiktionary.org/wiki/routine
b) machine /məˈʃiːn/ https://en.wiktionary.org/wiki/machine
2) Words correctly coded /ɪ/ for "i"
a) big /bɪɡ/ https://en.wiktionary.org/wiki/big
b) pin /pɪn/ https://en.wiktionary.org/wiki/pin
3) This is especially confusing (http://dialectblog.com/2011/11/10/the-western-us-and-velars/)
"The word “English” is the one that causes the most confusion for me in IPA. I regularly see it written in IPA as /ˈɪŋɡlɪʃ/, and although that is much like RP, back in the San Joaquin Valley it’s definitely and clearly /ˈiŋɡlɪʃ/. At the very least, the first “E” and the middle “i” aren’t possibly the same vowel. I also would not call the second vowel /ɨ/, but it’s possible that I have trouble identifying /ɨ/ in my speech anyway (but the Rosa’s/roses difference helps)."
4) Evidence number 4 , A dictionary that writes it /iːŋk/
/i/ sound before "ng" and "nk"
5) YouTube /pijŋk/ not /pɪŋk/ song
Here is a typical American accent where the word "pink " is being used clearly using the /pijŋk/ .
https://www.youtube.com/watch?v=Asb8N0nz9OI
6) American Heritage Dictionary Pronunciation key: https://www.ahdictionary.com/application/resources/misc/pronkey.pdf
Why is "bee" \bi\ and not \bi:\ ? Because Americans don't see the difference as a lengthening of time but as a change in tone.
CONCLUSION
Words like "pink" or "blink" and "english" should use the IPA markers /ijŋ/ ; when CLEARLY the "i" in these cases is not the /ɪ/ in pin, but CLEARLY is the /ij/ in machine or the "e" in "evening".
Solution 1:
When most people speak, I hear the same vowel in pink and pit. There are definitely some people from California who say peenk and keeng. And from the links you give, some people from Michigan do the same thing. For these speakers, the phoneme /ɪ/ changes to /iː/ before /ŋ/. This really isn't a problem for comprehension, because /iːŋ/ isn't present in any English words, so there are no minimal pairs.
In California, many people suspect this is due to the influence of Mexican accents.
At a wild guess, in Michigan it's related to the Northern Cities Vowel Shift.
Solution 2:
Hmmm...when is the last time any of you said the word "ink" in a sentence (before reading this question)? The last few instances I can remember myself are:
"The printer needs ink."
"My pen's out of ink."
"Do you sell printer ink?"
Now try saying:
"pink ink"
"color ink"
"squid ink"
"India ink"
Do you pronounce "ink" the same way in each variation of sets? I don't. My twenty-one year-old son doesn't either. We're both "native" speakers, although my mother's English was a heavily "accented" dialect, and I spoke only "twinspeak" for the first few years of my life, so my speech "native"ness and his differ.
But to the point of the OP question, I agree. I think for the sake of standardization, which is the purpose of dictionaries and the like, certain forms become calcified and canonized, and as actual variations continue to shift, the standard form retains tradition and loses correctness.
Check out this speech archive for a cool example of variation collection:
http://accent.gmu.edu/index.php
(I heard about the project on NPR - I'll try to find the link.)
http://m.wamu.org/#/programs/metro_connection/11/06/24/please_call_stella_the_speech_accent_archive_from_afrikaans_to_zulu