No, you do not have to be a good writer to be a good director.
Writing..., well, practical writing for self-direction, involves creativity of crafting a story with available or attainable resources; equipment, locations, cast and crew, budget, and time.
Mostly it's creativity + planning.
Directing is whole lot more difficult.
Thinking of stuff is nothing compared to actually doing it and spending money and social capital to make ideas reality.
Plus, there's managing the icky sloppyness of people.
A director has to manage cast and crew both on set and their schedules even getting them to the set - in addition managing materials.
Often writer-directors are also producers and (poor) promoters.
Thinking up of sh!t is relatively easy.
Actually getting something made is considerably more difficult.
In other words a great screenwriter with hard drive gold is less valuable than a poor director getting lousy product to market.