Your basic premise is incorrect here: /w/ is listed in the Consonant section of the IPA page on Wikipedia, under Co-articulated consonants where it belongs.

It doesn’t belong in the main table, because the main table orders consonants by place of articulation, and /w/ (like all co-articulated consonants) has multiple places of articulation: bilabial and velar, which are eight columns apart in the main table. You could of course add extra columns to the table for combined places of articulation, but that would make the table huge, unwieldy, much less clear and consistent, and much less useful.

So yes, there’s a good reason it’s not included in the main table of pulmonic consonants: there’s no place to put it without ruining the table.

Your basic premise is incorrect here: /w/ is listed in the Consonant section of the IPA page on Wikipedia, under Co-articulated consonants where it belongs.

It doesn’t belong in the main table, because the main table orders consonants by place of articulation, and /w/ (like all co-articulated consonants) has multiple places of articulation: bilabial and velar, which are eight columns apart in the main table. You could of course add extra columns to the table for combined places of articulation, but that would make the table huge, unwieldy, much less clear and consistent, and much less useful.

So yes, there’s a good reason it’s not included in the main table of pulmonic consonants: there’s no place to put it without ruining the table.