Design Doc matters because design docs reduce expensive rewrites by exposing tradeoffs early. It gives builders a precise word for the thing they are changing, debugging, reviewing, or shipping.
ELI5
Think of Design Doc as a repeatable work method. It gives one small job a clear name so the whole app is easier to understand.
In practice
Use it to make work repeatable, reviewable, and auditable. In practice, name the owner, input, output, failure mode, and proof before relying on Design Doc.