The poem's title, “No Rest for the Idle”, is an allusion to the phrase "no rest for the wicked", which derives from Isaiah 57:20-21:
But the wicked are tossed like the sea; for it is not able to keep still, and its waters toss up mire and mud.
“Yet[c] there is no peace,” says my God, “for the wicked.”
The title is also reminiscent of the idea that idleness may be masked under the cloak of work (or busybodying). See for example 1 Timothy 5:13:
At the same time, they also learn how to be lazy while going from house to house. Not only this, but they even become gossips and keep busy by interfering in other people’s lives, saying things they should not say.
See also 2 Thessalonians 3:11
We hear that some of you are living in idleness. You are not busy working—you are busy interfering[c] in other people’s lives!
Matthew Arnold's father Thomas Arnold, headmaster of Rugby School, once said in one of his sermons in Christian Life (quoted from The Victorian Frame of Mind, 1830-1870 by Walter E. Houghton, page 245, emphasis mine),
Do we not know … that every idle moment is treason; that now it is the time for unceasing efforts; …?
The entire poem present idleness as an ocean without shores, without recognisable features, without tides or waves that carry the idle in a specific direction (a sea very different from that in Isaiah 57:20); in other words, there is no escape from it. At the same time, however, the idle must continue to ply the oars.
The same contrast between idleness and work can also be found in Matthew Arnold's life and work. Several of his poems evoke idle contemplation; see for example The Scholar-Gipsy ("Here, where the reaper was at work of late—/ … / Here will I sit and wait, / While to my ear from uplands far away / The bleating of the folded flocks is borne") and Lines Written in Kensington Gardens ("In this lone, open glade I lie, …). In his life, by contrast, he was very busy. Nathan Haskell Dole wrote in his Biographical Introduction to The poetical works of Matthew Arnold (1897),
His capacity for work was extraordinary. Occasionally in his letters he hints at the demands upon him. We catch glimpses of him examining half a dozen schools in a day, looking over scores of examination papers, putting his hand to the stores of his well-ordered mind to write reviews or essays for magazines, preparing his Oxford lectures; yet never, amid all the rush of his busy existence, did he neglect the claims of his dearly beloved family, (…)
(Ironically, perhaps, as a schoolboy Matthew Arnold was called idle. See The Triumph of Matthew Arnold by Noel Annan, New York Review of Books, 1981.)
According to Richard Adelman (Idleness and Aesthetic Consciousness, 1815–1900, Cambridge University Press, 2018, page 105),
[Matthew Arnold's] early poetry repeatedly dramatizes idle aesthetic contemplation in accordance with various Romantic models, but always does so in order to stress its inapplicability to—or impossibility in—the present.
Even though Arnold wrote about idle contemplation, he avoided the trap of idleness in his own life. The idle in Kay Ryan's poem have no Matthew Arnold to inspire them to escape from idleness.