Objection, your honor! Question assumes facts not in evidence.
I agree that it would be sad if poetry became, as mathematics and philosophy have become, the preserve of a narrow class of professionals. (That path was inevitable for mathematics, of course; I still have hopes tha philosophy may escape the tyranny of the journal article and go back to being a part of the general culture rather than a cult of specialists and a small group of non-professional fans like me.)
But the phenomenon of marginalization applies only to one sort of poetry: the sort designed primarily to be read on the printed page. That sort of poetry was only a popular art form during the historically brief period between the introduction of mass literacy and the invention of radio.
For a much longer sweep of history poetry was performed, not read, and usually to music: the bard carries a harp, not a pen. Robert Burns was perhaps the last important poet, as the poetry professors define poetry, to write mostly words for songs. But of course songwriting didn’t die, or become an abstruse art form.
If you want to complain that contemporary lyricists aren’t up to the Burns standard, I’ll mostly agree with you. But that’s a complaint that contemporary poetry isn’t as good as poetry once was, not that “poetry has ceased to matter.” To deny that Cole Porter or Bob Dylan or Paul Simon or Joni Mitchell or [your favorite rapper’s name here] function as poets is mere confusion or misplaced snobbery.
Now, why academic students of poetry and complilers of anthologies choose to ignore all the songwriters since Burns is a different question, and perhaps one worth working on. (To my ear, “Urge for Going” is a great poem, even without Tom Rush on the guitar.) But poetry, like its relative music, is too basic a part of human experience to ever fade away.
Whether those of us who treasure poetry-not-set-to-music can hope for the appearance of another Cummings or Auden as part of the return of a culture where printed-page poetry is common currency among educated people is, again, a different question: I agree with Gioia that the radio (to which I would add the audio-book) might be one key to such a renaissance. But surely that question is far less important than the question “Can Poetry Matter?” It never stopped mattering, and it never will.
Footnote And yes, people are still writing excellent verse not designed merely to be read by other poets: Teresa Cader, for example.