We write design docs at Google to communicate ideas with each other. They're useful for promo committees because effective communication between engineers is something that is prerequisite for effective engineering.
Of course a full design doc is not needed for every change. Many changes are small and straightforward. Only big things, where the team needs to discuss and understand options. Or bigger things, where directors etc need to sign off (not really design docs anymore, but same basic thing).
The fact is that, on average, design doc+code takes less time than code without design (that is, without communication). Again, only for certain kinds of changes. Things go faster because problems are found, approaches are adjusted, or unmotivated features are axed.
Of course a full design doc is not needed for every change. Many changes are small and straightforward. Only big things, where the team needs to discuss and understand options. Or bigger things, where directors etc need to sign off (not really design docs anymore, but same basic thing).
The fact is that, on average, design doc+code takes less time than code without design (that is, without communication). Again, only for certain kinds of changes. Things go faster because problems are found, approaches are adjusted, or unmotivated features are axed.