Why water won't dissociate more?
The energy required to break the first $\ce{H-O}$ bond in water is $\pu{493 kJ/mol}$. For comparison, the energy required to break the first $\ce{H-C}$ bond in methane is only $\pu{435 kJ/mol}$. As a point of reference for just what these numbers mean in terms of bond strength, we can think about how long it takes for methane to be destroyed in the atmosphere. The first step of the destruction of atmospheric methane is to break that first $\ce{H-C}$ bond; because this is so difficult to do (again, requiring $\pu{435 kJ/mol}$) it takes an average of about 9 years for a molecule of methane to be destroyed! And the energy required to break the $\ce{H-O}$ bond in water to form hydroxide and hydronium ions is even greater.  

I realize that my analogies involve very different processes, but the underlying issue in both cases (atmospheric destruction of methane and self ionization of water) is bond strength. I hope that this gives some insight as to why the self-ionization of water is as low as it is. Don't hesitate to ask for any clarifications in the comments.