The standard error of a proportion will be the largest it can be for a given N when the proportion in question is 0.5, and gets smaller the further the proportion is from 0.5. I can see why this is so when I look at the equation for the standard error of a proportion, but I can't explain this any further.

Is there an explanation beyond the mathematical properties of the formula? If so, why is there less uncertainty around estimated proportions (for a given N) as they get closer to 0 or 1?