Why does the diphthong /aʊ/ not occur before /k/, /m/, /p/, /b/, /g/ etc?

I actually wrote a long post about this topic on the Linguistics SE site: you can see it at Why English is missing some phoneme sequences (/aʊv/ or /aʊp/).

Incidentally, trauma is only pronounced with /aʊ/ when it is given a "foreignizing" pronunciation. The anglicized pronunciation uses the thought vowel, the usual pronunciation of the digraph "au" in English.

As you may know, a major source of Modern English /aʊ/ is the Middle English long vowel /uː/, which changed to /aʊ/ as part of the "Great Vowel Shift". For some reason, /uː/ did not undergo this change before a labial consonant (p b m f v): it was either retained as /uː/ (as in room) or in some cases shortened to /ʌ/ or /ʊ/.

The velars are a bit harder to explain. It seems like for /g/, there just weren't many words of the appropriate form to historically lead to a sequence of /aʊg/, but there are some words where shortening seems to have occurred to /uː/ before /k/.

A general pattern seen in English and in some other languages also is that more complexity is allowed in syllables ending with a coronal consonant (d t s n tʃ l all fall in that category) than in syllables ending with another kind of consonant. This more theoretical, abstract point might help explain the pattern of which syllables /aʊ/ is restricted to, although this point doesn't clearly explain why other diphthongs such as /aɪ/ are not restricted the same way (/aɪm/ and /aɪk/ are frequently found in English words).