The layout of an IPA chart is partly arbitrary, by which I mean that there are patterns to it, but those patterns aren't necessary the only patterns that would have been reasonable. They just are what they are. I don't think you'll learn much about linguistics itself (as opposed to the history of linguistics) from trying to study them. The official chart has been revised several times.
The Wikipedia article "History of the International Phonetic Alphabet" shows that ⟨w⟩ has variously been placed under the labial or velar columns in past charts.
E.g. there is a chart published in 1912 where ⟨w⟩ is listed in the same column as ⟨p b m⟩. You can see it here.
If you want to make your own chart with a column for /w/, you can do that. It just will be different from the most recently published official chart from the International Phonetic Association. (Unless you become a member of the IPA Council or otherwise manage to convince them to publish a revised chart with a column for /w/.) Many people, including many linguists, sometimes use IPA symbols in non-official ways: it's not a big deal to make a chart with non-official ordering of IPA symbols.
The article you linked to states "The main chart includes only consonants with a single place of articulation." That is an explanation of sorts. I don't know whether there are records of any more detailed considerations made by the IPA.
The Wikipedia article does include ⟨w⟩ in the "Consonant" section. That section has the subheaders Pulmonic consonants, Non-pulmonic consonants, Affricates, Co-articulated consonants. It shows these as sections above each other; the IPA presents the different sections on a page. The complete chart includes all of them. Wikipedia adds some symbol + diacritic combinations to its charts.
The chart that you've been looking at is not an "English IPA table"; it's just an IPA table. If you look at the table used in the Wikipedia article "English phonology", /w/ is charted as the intersection of the "velar" column and approximant row, which works because English does not have a non-labialized velar approximant to contrast with /w/. That's different from what you'll see in the official IPA chart; however, if the reader can understand it, why does that matter?