What hope is here for modern rhyme To him, who turns a musing eye On songs, and deeds, and lives, that lie Foreshorten'd in the tract of time?
These mortal lullabies of pain May bind a book, may line a box, May serve to curl a maiden's locks; Or when a thousand moons shall wane
A man upon a stall may find, And, passing, turn the page that tells A grief, then changed to something else, Sung by a long-forgotten mind.
But what of that? My darken'd ways Shall ring with music all the same; To breathe my loss is more than fame, To utter love more sweet than praise.
And now our Tenny gets even more emo. If all of those really great poems and songs can't be remembered in the vastness of time, there's no hope at all for "modern rhyme," which he seems to consider less than the old greats.
Modern poems, like Tennyson's own "lullabies of pain" (the very elegy you are reading) are only good to bind books, line boxes, or to be used as a way to curl a girl's hair.
No matter—Tennyson's still going to keep on getting his poetry on. He's not worried about getting famous.
His poem helps him cope with his loss because it allows him to express his love for Arthur.