Hymns that are Prayers to Jesus

I've heard some Christians say that it is inappropriate to pray to Jesus. One of the papers on this website refutes that claim.  Following is a brief excerpt from that paper:

 If it were wrong to pray to Jesus (and the Spirit), it would be wrong to sing many of the hymns in our songbooks. Having gone through about ½ of a hymnbook I have, I discovered many songs we should take out if it is wrong to pray to Jesus and the Spirit. Below are some examples of these songs (with their “offending” text). 

 Love Divine All Loves Excelling

…Jesus, Thou art all compassion; Pure, unbounded love Thou art.
Visit us with Thy salvation; Enter every trembling heart.

Jesus, Lover of My Soul

…let me to thy bosom fly
…Hide me, O my Savior, hide
…Oh, receive my soul at last!

More Love to Thee

…O Christ, more love to Thee!
Hear Thou the prayer I make on bended knee.
This is my earnest plea: More love, O Christ, to Thee.

Close to Thee

Thou, my everlasting portion, More than friend or life to me,
All along my pilgrim journey, Savior, let me walk with Thee.
Close to Thee…

My Jesus, I Love Thee

…I know Thou art mine.
For Thee all the follies of sin I resign.
My gracious Redeemer, my Savior art Thou. 
If ever I loved Thee, my Jesus, ‘tis now.

My Faith Looks Up to Thee

…Thou Lamb of Calvary, Savior divine!
Now hear me while I pray; Take all my guilt away.
Oh, let me from this day Be wholly Thine!

Come, Holy Ghost, Our Hearts Inspire

…Let us Thine influence prove:
Source of the old prophetic fire.
Fountain of life and love.