Henry implies that the poetry of "theme & subject-matter & more direct speech" has been swept away by the triumphant barbarians of the avant-garde, who now hold sway over the holy poetic empire. It's an idea I see popping up in a lot of poetry debates, even (especially?) among self-identified avant-gardists: maybe we've swung too far in this direction, maybe we need to "go back to" ______ (speech, feeling, love, lyric, etc.).
Anybody read the New Yorker recently? Poetry? American Poetry Review? I don't think the speech-based thematic poem is under any particular threat. (If it were, I might say good riddance, but that's another story.) Nor do I think the alleged victory of the avant-garde is so total. Locally? Sure, experimental types have found sinecures here and there, established presses, journals, even whole academic programs. But the face of poetry that "most people" see, even most people who study poetry in college, if they see any at all, isn't one that strikes me as dominated by the avant-garde.
The anxiety over poetry communicating to a coterie rather than to a wide audience has been with us at least since Wordsworth, and probably since Milton. I don't think we're going to win a big new audience for poetry by writing like Billy Collins.