Why does 写 not have a dot on top?
The, new, Outliers dictionary provides some insight as to how 寫 became 写:

FORM
写 is shorthand for 寫. The top part, 冖, is a common abbreviation for 宀. The bottom part is a shorthand abbreviation for 舄 (see the diagram below for how that works).


which is referenced from:

邵源、邵冠勇，2010《簡化漢字解說》，济南：齐鲁书社 2010年12月第一版。

It also continues:

COMPONENTS
冖
In 写, 冖 is an empty component. It was originally 宀 “building,” a meaning component, hinting at the original meaning “to move something from one location to another.”

The simplified version is just simply old shorthand that was in turn made into a Chinese simplified character.