In the context of the poem, which books should burn?

According to Stafford's poem, "truth, brittle and faint, burns easily." These are the books which will first begin crumbling away. However, the speaker goes on to identify certain books which "ought to burn"—those which are "trying for character but just faking it." These books, we can interpret from context, are those that the speaker feels do not contain sufficient "character" to justify their existence, particularly if they are "faking" the message they are trying to convey.
Worse than these books, though, are the ones which have never been written, "whole libraries" which are representative of our communal ignorance. Ignorance not committed to paper cannot be subjected to the fire, yet "ignorance can dance in the absence of fire."
This is an interesting poem because it turns on its head the general association between book burning and censorship, forcing us to consider the true value of the books we read and how these relate to our ignorance as a society.