To comment on the notion that postmodern poets are entrapped by the legacy of traditional and modernist poetry, as well as the demands of their own lives, one should probably identify a postmodern poem of interest and discuss how it affirms or deviates from the statement.
One famous postmodern poem is “Howl” by Allen Ginsberg. This poem contains many of the thematic hallmarks of postmodern poetry, including alienation, displacement, and a departure from traditional language and values. The poem was published in 1956; it caused quite a stir and was put on trial for violating obscenity laws.
Despite its avant-garde attributes, it’s possible to claim that this poem is entrapped by the legacy of past poets. The protruding lines connect to the long lines in Walt Whitman’s poems. Whitman himself used long lines in free verse to push back against the poetic conventions of his own time, so it seems appropriate that Ginsberg would do something similar for a similar reason. The recurrence of “who” continues a legacy of heavy repetition and anaphora featured prominently in more traditional poetry, as Edgar Allan Poe does in his poem “Annabel Lee”—Ginsberg even explicitly references Poe in “Howl.” Additionally, Ginsberg’s fragmented, unsettling portrayal of society might make some think of T. S. Eliot’s modernist poem The Waste Land.
As for the idea that Ginsberg is entrapped by the demands of his own life, it’s reasonable to argue that Ginsberg feels propelled to express his and friends’ intimate experiences. After all, "Howl" begins with, “I saw the best minds of my generation.” The “who” seems to refer to people that he personally knew or, sometimes, himself.
If talking about “Howl” isn’t appealing, think about putting the statement in conversation with Diane di Prima’s “An Exercise in Love” or Amiri Baraka’s “Babylon Revisited.” These are two postmodern poems that support that notion that postmodern poets are inevitably snared by a mixture of poetical lineage and their own personal lives.