If you don't like the game design.. Find another game designer who has something of your interest.
You could become a game designer yourself.. but I haven't seen any programmers who are good game designers.
Programmers have a bad habit of just going with the flow since they can code instantly whatever ideas pop into their head.
And they only make mediocre GDD's because of this.. if they make one at all.
I think you're too hung up on the importance of a GDD. If you'd studied software development you would know about agile development methods, a fairly new way of structuring development. An emphasis is made on evolving requirements and producing code that can be quickly modified as a result. Unit tests and good (software) design patterns are used to help ensure code quality and maintainability.
Agile methods typically dispose of the monolithic design document, as they are often outdated by changes during development. The substitute used varies between specific methods, but typically a looser collection of requirements are used that can be easily rearranged and modified.
I frankly don't care if a game designer can write a GDD. I care if they can effectively organize and communicate an idea using whatever medium is best suited to the task at hand.
I can give a personal example of evolving design from my own project. (a 2D space trading game for context)
When I started I wrote out 5 or so pages of design, not comprehensive but enough to communicate the idea. I then started work. A few weeks in I hit a roadblock. My design called for large systems where the player could fly freely around. This didn't work (the engine I was using couldn't handle the large images for planets, and they took too long to procedurally generate).
So I changed the design, split off the navigation and battle into separate parts. This gave my an opportunity to try Newtonian physics in combat, since it wouldn't complicate the navigation.
A few weeks later I had Newtonian combat. Turns out, it wasn't very fun, and I spent a lot of time writing helpers for the player (leading targets, missile tracking, etc) to make the game playable.
So I redesigned it to a more stylized combat. Ships now flew about like it was the 18th century and broadsides were all the rage. This turned out to be quite fun, but a little limiting. The player only controlled one ship and sometimes you could get swarmed by enemies if your AI team-mates abandoned you.
So I redesigned it. When I'm done with the current prototype the player will control his entire fleet directly. Essentially a 2D space RTS with ships pretending it's the 1700s. Hopefully it will be fun, if it isn't I'll redesign it again.
I'm not claiming to be a great designer, just showing that unforeseen roadblocks (the technical issue, or combat not being fun) can force a redesign, and you shouldn't be afraid of it. Embrace it as a chance to experiment and learn.
(sorry if that rambled a little off topic)