The songs I'm thinking of are mostly from the British art song period - from the very late 19th century into the first few decades of the 20th, but the same thing applies to much German lieder. The composers are remembered, and there's information about them online - often at length. But the poets are almost entirely forgotten, in spite of having produced reams of poetry, or twenty or thirty novels, or various other writings in their lifetime. And even if the poets are still visible online, their work is forgotten: a mere list of names of books that few libraries would have copies of.
Billy Collins wrote a delightful poem called Marginalia, about the sorts of things that people scribble in the margins of books. In one stanza he writes:
Even Irish monks in their cold scriptoriajotted along the borders of the Gospelsbrief asides about the pains of copying,a bird singing near their window,or the sunlight that illuminated the page -anonymous men hitching a ride into the future on a vessel more lasting than themselves.Those last two lines are apt for what I've written above: like those Irish monks, the names of the poets would be forgotten if it wasn't for the vessel, the composer (or perhaps the song), being more lasting than themselves.