When answering a question like this, it's worth being aware of the backstory of Fahrenheit 451, at least as it was described by Beatty. As Beatty tells it, the infantilization of society was not actually an initiative directed by the government. Rather, this evolution occurred within the society itself as it became increasingly shaped by consumerism and a culture of gratification.

With this in mind, we can find a potential in-universe rationale to answer your second question, as to why contemporary literature goes largely unmentioned within this world. That being said: be aware that, just as Fahrenheit 451 ultimately envisions an alternate history, this answer will likewise need to reflect that trajectory which Bradbury foresaw, rather than the reality that has followed the book's publication.

In any case, if we assume the history described by Beatty really did happen—society itself became increasingly driven by gratification and increasingly hostile toward the very thought of being challenged by the products it consumed—then we can expect these trends to have had a dramatic effect on the literature this society produced. If a society grew so intensely hostile toward consuming literature, then this question arises: how many writers should we expect to find continuing to produce literature in such a world (and how many of those would we expect to see published)?

The books that Montag, at the end of the novel, learned were saved and memorized, include what in the 1950s would have been considered the "great books." These works were considered to contain the best and highest of human thought. Interestingly, they include works by philosophers such as Socrates, books by scientists such as Darwin and Einstein, books by political figures such as Lincoln, and great religious texts. Granger also mentions some literature, such as Gulliver's Travels, a book which also happens to be a political and social satire, and Byron's poetry.

In the 1950s, Einstein's work would have been relatively recent, but clearly there can be no books mentioned that did not exist when Bradbury wrote his novel.

The books that are considered valuable represent a diverse set of conflicting viewpoints and therefore invite debate. Machiavelli, for example, would differ with Christ and Gandhi on the best way to run a society. All these books were written as well by figures who were fearless in rejecting orthodoxy and thinking for themselves so that they advanced human knowledge and freedom—just what the world of book-burning does not do. They are also an interesting snapshot of the 1950s, as they include no books by women or black people, although a few Asian authors are in the mix.

If you woke up one day to discover that the government and everyone in society were burning books, which ones would you save? Of course, most people would save their favorite books. However, for the intellectuals that Montag meets after escaping from such a society, they choose the following books to save through memorization:

"I am Plato's Republic. Like to read Marcus Aurelius? Mr. Simmons is Marcus . . . I want you to meet Jonathan Swift, the author of that evil political book, Gulliver's Travels! And this other fellow is Charles Darwin, and this one is Schopenhauer, and this one is Einstein, and this one here at my elbow is Mr. Alber Schweitzer, a very kind philosopher indeed. Here we all are, Montag. Aristophanes and Mahatma Gandhi and Gautama Buddha and Confucius and Thomas Love Peacock and Thomas Jefferson and Mr. Lincoln if you please. We are also Matthew, Mark, Luke, and John" (151).

Within the above list are some of the greatest writers, philosophers, political leaders, spiritual leaders, and scientists to grace the earth with human thought. If all of these works are lost, it would mean that humanity would have to rediscover such genius again. That might take centuries! Also, Bradbury wrote Fahrenheit 451 in the early 1950s, so anything written after its publication would certainly not be included. However, these intellectuals must have memorized the above list of works because they all have something in common--they are all classic works that not only contain a store of human knowledge and wisdom, but also provide different perspectives on how to live, how to create a free and just society, and how to question the status quo. The society in Fahrenheit 451 uses manipulation and distraction to control the population. Thus, the works memorized would be useful if that society were ever in a position to rebuild. Soon after Montag meets these men, an atomic bomb goes off. Apparently, the time to rebuild and use these valuable works of information and insight might be closer than they realized.