They do not sing from a place of power, but of hope. They don't have a sense of present salvation and a close walk with The Lord, but of going to heaven to be with Him after they have died. IOW, it is a false gospel that they have believed, that has not united them with their maker, but they have instead entered a covenant with death (language from Isaiah 28:15).
As a consequence, they cannot sing lyrics with a conviction of that reality, whereas it is clear through the dense doctrine of the hymns that the faith of our forefathers had found that reality of The Gospel.
For example, compare the lyrics of your modern worship music to these ones. They are all speaking of having already become righteous, having already come to see Jesus face-to-face, whereas the modern ones speak of those things being a hope that they will never achieve in this life. It is simply a different spirit.
Turn your eyes upon Jesus,
Look full in His wonderful face,
And the things of earth will grow strangely dim,
In the light of His glory and grace
Hymn: Turn your eyes upon Jesus
Are you washed in the blood,
In the soul-cleansing blood of the Lamb?
Are your garments spotless? Are they white as snow?
Are you washed in the blood of the Lamb?
Hymn: Have you been to Jesus for the cleansing pow’r
Perfect submission, perfect delight,
Visions of rapture now burst on my sight;
Angels descending, bring from above
Echoes of mercy, whispers of love.
Hymn: Blessed assurance
My sin—oh, the bliss of this glorious thought—
My sin, not in part, but the whole,
Is nailed to His Cross, and I bear it no more;
Praise the Lord, praise the Lord, O my soul!
Hymn: It is well