I will start off by saying that i really like Game Design Documents. Especially for small games where you anticipate the game taking no longer than 6 months. In these types of games you will can reasonable predict what will need to be done to finish the game. This type of enviornment is what i think a GDD is best for.
Benefit #1: Allows you to clearly define your goals.
Most of the games i have worked on have been shorter games. I have made a couple casino games for the app Double Down Casino. When working on these games having a well defined GDD made it so that it was really easy to know what needed to be done and how to test for it. The GDD allows for an easy way to clearly define all your major goals for the game. This allows the whole team to be on the same page. The shorter the game the more reasonably you can predict what the end result of the game will look like.
Imagine a blackjack game. You know in your head all the pieces to a blackjack game. You could write a GDD that explains every task you will need to be able to do. For a game like Syrim that would be a lot harder. You can't reasonably know every little detail you will want to add to the game. You also can't fully know every level from the get go. You can iterate on the GDD for games like this which allows you to get most of the same benefits of a small game.
Benefit #2: Save time in the long run.
When every part of the team is on the same page this allows you to separate tasks for the game beautifully. The Art team can make all the assets needed at the beginning before the Developers get on which makes it so that the Developer isn't wasting time. This allows you to specialize in tasks if there are multiple people but if its just you also allows you know exactly what needs to be done.
When you know exactly what needs to be done you can be extremely efficient with your time. Sometimes when you are working on a game with no GDD you get to a point where you had been coding for hours trying to get that one feature correct. You finally get that feature but than you forgot what you need to do next. You then spend a couple minutes thinking of your next task. This is when you are most vulnerable to opening up Reddit and procrastinating. The GDD allows you to keep on task and look up another goal for the game quickly so you stay on task.
Benefit #3: Meet your deadline and avoid crunch time.
When you have a document that has clearly defined goals this allows you to avoid crunch times. Being able to know how much is left for a game to be complete allows you to mentally clock in or out. When you have little time left and many bugs this allows you to clock in and start to hammer out bugs. When you have little bugs left and the game is a bit further out than you can check out a little more. This is where you want to be. Use the GDD to your advantage to create yourself a cushion of breathing room to avoid crunch time.
I hope i have helped you realize some of the benefits of GDDs. Tell me in the comments any benefits you think i left out. Or tell me if you disagree with any of the benefits i mentioned. Have a wonderful day!