I don't think that each and every song that is sung from the heart of a believer to the Lord must meet always meet the exact definition of "worship" or "praise." I think that there is space in spiritual music for learning (many Sunday School Bible Songs come to mind), for example. And for the pouring out of one's heart and soul to God Almighty. We have the Psalms to look to for an example of this.
Col 3:16 "Let the word of Christ dwell in you richly in all wisdom; teaching and
admonishing one another in psalms and hymns and spiritual songs, singing with
grace in your hearts to the Lord."
I do think, however, that "worship" is another word that should not applied so generally to music that it may or may not apply to. To worship means to adore, respect, venerate, be in awe of, honor. To worship someone puts the focus on the person being worshipped, not on the person who is praising. To expound on the amazing qualities of God and stand in awe of His glory is a great thing. When we read worshipful sections of the Bible, we are often brought away from the narratives, away from the teller of the story, away from the world. Worship is not about the experience of worship. It is not about what it does to the person. It is tempting to get caught in that creation, the feelings that accompany true worship. Just as it has been tempting for many to be caught in worshiping any part of the creation rather than the Creator.
But to sing a song about the experience of "worship" and then call that song "praise" or "worship".... this seems to be inaccurate and bizarre. More than that, wouldn't it make it much more difficult to recognize real worship? What exactly is that point of this? Aren't we supposed to be watchful, diligent, and mindful?
"God is a Spirit: and they that worship him must
worship him in spirit and in truth." John 4:24
Truth should permeate worship: in it's content, in it's categorization, in the spirits of the worshippers.
Psalm 29 and Psalm 96 are really amazing examples of this.