I have often found that I used to read books aimlessly, almost without accumulating culture. I have found, for example, modernist literature powerful but shallow in some sense, and that is because I had not read a tradition that comes before it. For example, I believe that I can get more out of Kafka given that I have read Homer before, and so it is part of this project to get an overall culture that satisfies the variety of human values and sentiments. The quest for meaning, for example, was never as eloquently and explicitly spoken of than in religious texts, and there is thus something to get out of them before reading atheistic searches for meaning that populate our modernist literature.
Of course, one might agree and disagree on specific ommissions/inclusions, but as a newb I find this list quite useful. I am only starting the Theocratic age now and I had not heard of most of these works, and those I had heard of I never would have had the motivation to read, like Homer or even the Jewish and Christian bible.
Homer is Homer exactly because nobody needs to read him to relate to his tradition in some modernized sense. Anyways, you will never read Homer, you are reading the specific traditions of his translations. There is no way you will not feel how well Chapman translate the dialogues inside the Iliad, specially considering he belongs to the Shakespearean time.
Anyways, sometimes chronology has little to do with the influence of a text, you can basically ignore all Homer for all Medieval literature and stick to Virgil and mostly Ovid's Metamorphosis. This will be true until the romantic age, when there was enough greek translations of Homer to make his direct influence that relevant. Still, those two level of influence is up there with the Bible. Which is a problem of Bloom's list... It does guide blindly.
As the list of modern times, you think USA is over represented, Andy? Look the number of jewish authors that obviously almost nobody heard about and Bloom lists. He is an anglophobe, beyond that area there is a lot of blanks reggard his knowledge. The Latim American list (which he groups in a single tradition, which would be the same as putting together Spain-Portugal or France-Germany) is as flawed as one can get too.
With old age, he became obssessed with academic feuds against the feminist/political correct/african/neo-marxism reading of the canon (the battle against the white male writer) and less of a critic. Together with this, he also turned in a new-spiritual path, searching his jewish origens... Those bias are all in the list.