For Monte Carlo simulations, or any other numerical methods that rely heavily on the quality of the pseudo-random numbers generated (i.e even/desired distribution on a certain domain) for that matter, why aren't evenly-spaced and perfectly/accurately distributed numbers (not pseudo-random) used as opposed to pseudo-random numbers?
The reason I ask this is because I would imagine the main purpose of sampling tons of pseudo-random data as opposed to non-random data would be to speed up the time taken by the program that is sampling that data, much like how throwing a bunch of paintballs at a canvas/wall would, more easily and quickly, cover up that canvas/wall than carefully painting it with a paintbrush would. However, many pseudo-random number generator algorithms that I have seen look more complicated and time-consuming than just using non-pseudo-random, perfectly distributed data.
Clearly I have a misunderstanding of this topic. Could anybody help clear this issue up?