Mesora: I believe it is to signify that the purpose of all creation is the glorification of God. By including each letter of the aleph bais in these Psalms, David wished to display in other words, that all creation, (indicated by every letter being present) is solely for the purpose of acknowledging and glorifying God.
Instead of listing every created thing and showing how it is for the purpose of acknowledging the Creator, an impossibility, David chose the method of representing all creation by including each letter. As every letter is accounted for, it means to say that just as all letters are here in praise of God, so all matter whose names fall under each of these letters, has its purpose the glory of God.
I am not aware why David didn't just say so, instead of engaging the alphabetic, acrostic methodology. The fact is that the drafters of our prayers did say this in Nishmas Kol Chai.
Perhaps David desired that the breadth and magnitude of scope be expressed, as he was attempting to display that ALL matter only has purpose with its glorification of God. A mere statement, perhaps, would not emote a reader to the fullest extent of appreciating such a concept unless each letter of the Hebrew alphabet was represented. Such an extreme show would effectuate in man an emotional response which David desired.