In my mind, randomness is irreplaceable in table top roleplaying for at least two important reasons.
The dice are more creative than me
Explaining results that arise randomly force us to stretch and go places a rational planning mind would likely never go. An example that I think is fitting is a hireling rolled up using my Hireling Traits Spur resulted in having "missing feet." I would have never made a hireling with physical disabilities available myself. And that seems a shame, because that hireling might be most likely to risk the dungeon to try and eke out a living. And that's the rationale our group came up with: previous hireling death and the risk of this particular dungeon meant only the most desperate were available for hire.
That leads to a subpoint of this: by having the random results generated in the open, collaboratively, it allowed the group to help me explain the random result and the group is more creative than me as well. In fact, I can't think of a way to bring the group in more to the shaping of your world. A DM who pre-plans everything, or follows an adventure path only allows the players to express crativity in what their characters do, what they say, what they steal, what they burn down. I think its cool if you could solicit ideas from the group: "Why would this be here?" In fact I often do something like that in post-play chatting.
The dice are smarter than me
I don't want to be responsible for your player's death. I don't want to be responsible for creating an expected course of events that will be the exact amount of tension, danger, speed, fighting, and treasure. What I mean is, I realize it is my responsibility as a DM to have a rough amount of treasure/monsters/empty rooms available in proportions that we know from experience are generally satisfying, but I don't want to be plotting a movie: first they'll fight the trolls, then over the waterfall, find the magic sword, cue closing credits.
Why, because it is impossible. Okay, maybe it's possible, but it only if you are really good, have a lot of experience, know your players, and then get lucky: Whoops, I expected you to take those trolls easy, you'll miss the waterfall now . . .
I will never be able to perfectly predict what the players will feel like doing, how they might try to solve problems they will face, or, especially, what course of event will please them most. Randomness lets me unshoulder this responsibility. Certain things are likely to happen, there are clues and indications in the game to these more likely events and players are free to choose a course with this fate-filled world.
An example of how I tried to negotiate this just recently was in my tomb complex. I decided on a pattern that Mahbit tombs would follow, including 2 false burial chambers for every person buried. I pretty much determined the condition of the tombs ahead of time-- flooded, collapsed, looted, pristine-- and I had a general level of danger/reward in each.
Then I rolled randomly to determine which of the three chambers in each tomb of the complex was the actual burial chamber of each ancient scholar.
Finally, I knew I wanted the four ancient scholars buried in this tomb complex to have 1 of four magic items and a possibility of having the main quest item. I rolled randomly to determine this during play when the characters breached the first real burial chamber. This way I didn't have any expectations as to which way the characters should/would go. I wouldn't be displaying facial tics or signs of impatience if the players were wasting time in the wrong area of the dungeon. And, hell, it was more fun for me, after 2 failed attempts at the complex would this party waltz in and find the quest item in the first place they tried? Nope, not this time.