On second thoughts, I will not do what I promised last time. Instead, I will quote the massive Historian of the Roman Rite, J A Jungmann, because, surprisingly, he says what I want to say so much better than I could say it.
He is writing about the Gloria in excelsis, but what he says applies very neatly also to the Canon.
" ... some commentators ... make excuses for the fact that the Holy Ghost is mentioned only at the very end, and then only in passing ... No, God and Christ are the pillars of the Christian order of the universe: God, the beginning and the end of all things, towards whom all religious seeking is bent and all prayer eventually is turned; but in the Christian order also Christ, the way, the road on which all our God-seeking must be directed. Therefore in St Paul's letters we find this duality of God and Christ not only in the introductory salutation, but time and time again throughout the writing. And if at times St Paul rounds out the duality and completes it in the Trinity, this is done not so much to acknowledge the three divine Persons themselves, as, rather, to mark more distiunctly the structure of the Christian order of salvation, in which our ascent to God is vouchsafed through Christ in the Holy Spirit.".
Perhaps I may put it crudely: if someone asks you what you have been doing all day, you don't say "Breathing". You assume that as the background, indeed, as an essential presupposition, to your activities. And Pneuma is the Greek for ... among a number of other things ... Breath.
In the next part of this, I give some doctrinal background..