When I first read the title, I had Jockers flashbacks. "Historical periods still matter, and will always matter," ran through my New Historicist-head at least twice. Add the current worries of what exactly "restructuring" means to my admittedly conservative fatigue over constantly having to defend close reading against these DH scholars, and I didn't have any patience going into the Underwood.
As Underwood gets into his argument though, it makes sense. The title is not nearly as inflammatory as I'm sure he knew it would be, either. Scholars starting back in the 1840's put forward this idea that historical periods mattered as a way to reinforce our own claims as a field that we matter. (He doesn't explicitly mention the concept of 'deep history' from what I recall, but they used it in the Victorian period to reference a period of time long past that we have evolved past. It was a professional response to the worry that evolution meant we were linked to the cavemen of long ago in some kind of irredeemable way. It was an early attempt by Victorians to relegate themselves to a new, modern humanity and a new, modern history. So it makes sense that the English department concept of historical divisions were birthed in the 1840s.) If we do not need to defend our field as "mattering," or if we have another way to defend ourselves against the constant threat of "restructuring," then sure. Historical periods no longer matter.
This is where he makes his most attractive claim, though I don't know if it actually stands on its own merits. I still have to think on that. At any rate, English doesn't need to use historical periods to defend itself as a field anymore because, instead, it can use interdisciplinarity to do so. As he closes the piece, someone has to teach students how to take into account cultural and historical considerations when reading and analysing literature. Might as well as be us. And we might as well add in a bit of quantitative analysis alongside our literary, psychological, sociological, historical, and economic theory. The reason I don't know if this works or not as a theory is that he doesn't seem to be arguing for an English department as much as he is arguing for a Liberal Arts department. He would handwave this criticism away as a slippery-slope worry, but I'm not sure that is enough. And this is coming from someone whose DH project for this class is essentially a history project with only a passing nod to literature.