Keep in mind, working with what wound up in the Bible alone, we only have a few hours' worth of information on the life of Jesus of Nazareth. The dude was a freaking rabbi. There had to have been more to his teachings, never mind conversations, jokes and witticisms. Think of how the evolution of Western culture would have changed if we had more specific writings from Jesus on, say, slavery, or homosexuality, or abortion, or women's rights.
Or gun control.
Scholars arguing against the existence of the Q Document rightfully point out that this would have been a hell of a thing for the early church to lose. And it would have been lost a long, long time ago. We can't even find records of people referring to the document, no matter how far back we go.
Either way, if the Q Document ever existed, it is likely gone forever; buried in the middle of the desert, or even worse... erased from memory.