In Fahrenheit 451 the past culture was eradicated. Why do you think culture and history is so important for us?
There are many reasons culture and history are so important, and your question can be answered generally or within the context of the novel.
Imagine that you, as part of a group, are elected to colonize a barren and uninhabited land. If you have no access to history and culture, what can you take with you to accomplish this mission? Nothing - not even the clothing on your back. You may have no matches, no flashlight, no seeds to plant, no farming implements, no reference books, and no watch or even a sundial. All of these are the creations of history and cultures past. You will literally have to re-invent the wheel, figure out the right kind of rock to strike a fire, assuming it occurs to you that fire might be created by man, try different kinds of plant materials or animal hides to cover your body, forage for food, use a trial and error method of discovering suitable building materials for shelter, and so on. Someone else has already done this work for you. Many other people have written books, painted great works of art, built tall buildings, created governments that function (mostly), gone to the moon, written symphonies, and figured out how to make some sick people well again. Man has progressed by building upon the work of his predecessors. What enables that to happen is language, first transmitted orally, then transmitted by books, and today transmitted via electronic impulses. And that brings me to the novel.
If you want to control people and make them satisfied with very little, what might be the best way to accomplish that? If they have no knowledge of the beauty and grace that life can offer, they will be settle for what is given to them. If they have no access to the ideas of others, they are less likely to speculate about what might be. Most of the glory, tragedy, and everyday life that is culture and history is given to us through writing. If you take away people's access to writing, you can control their minds and their hearts.