As we know, restriction of options is usually a spur to creativity rather than a hindrance. The narrower the scope in which your imagination is allowed to run riot, perversely, the more productive it usually becomes (within reason). An illustration: Give a man a pen and paper and he might spend 6 hours just thinking of something to write about. Give him a pen and paper and say "Write me a story about a murder" and he'll have a finished piece in half the time it took for him to even think of an idea in the first scenario.
Random generators are such a great aid to creativity, I think, because they embody this fundamental truth. They steer imagination and make it more productive. The simplest illustration of this is the random encounter in D&D (much maligned by people who don't actually really think about their gaming). Without random encounters, traditional games become stale and stressful for the DM, who has to spend unproductive and boring hours trying to think up interesting scenarios from the aether to entertain his players and keep the game going. With random encounters, his creativity becomes focused: why are these goblins here, and where have they come from? Bang: Focus. Interest. Post hoc narrative. Story. If he knows his game world reasonably well, he has it made.
This is also why generating random results on a table is enjoyable in its own right, even taken outside of the context of a game. I can't be the only person who feels this way - a peculiar glee in having a big set of d30 tables and just generating results to find out what happens. What is this treasure hoard, what is its history, and who put it here? What is this group of giants doing in this area, what are their names, and what do they own? What spells does this spellbook contain, and who is its original owner? Your imagination is steered, and consequently becomes productive, and the endorphines begin to flow.
Of course, without the ultimate random generators - players - even generating random results becomes boring after a while. Random generators need a game, just as games need random generators. It's a yin-yang thing, or something.