Is "poetry" irrelevant, or just the poems that people have classified as important? I don't think "poetry" can really be relevant or irrelevant, since to me it's simply a form of writing in which the structure is relevant as well as the content. On the other hand, poems from another era can hardly be faulted for not having the same impact today as they might have in the past. (Note that that "past" where they had an impact could still be years, decades, centuries after the poem was written!)

Dead Poets Society. A good poem does not need to be analyzed, and analyzation does not make a poem good. (That said, there have been occasions in which analyzing literature/poetry is interesting.)

I don't know what modern/contemporary poems you're referring too, but I would guess they don't all deserve this blanket ennui either. It's hard to write off an entire style as wasted.

But I'm not sure it was ever possible to make a living as a poet, purely. Poetry as a form of entertainment, that you could make a living on, maybe. But not all good poems are written for entertainment, and come with no guarantee of recompense. And did most people ever read poetry as succor? Or was it just something they were forced to swallow and spit out again, as necessary to be "cultured"? The latter is no benefit at all.

I'll close with something I got from my dad: In the beginning we had poetry, and that was rhythm. Then we added a tune, and got melody. Then someone realized physics was on our side, added more parts, and songs had harmony. ...Then, someone else found out that dissonance could be used to interesting effect sometimes, and we dropped back to melody. And today we have rap, and the human race has cycled back to rhythm.