That makes sense. Like a prototype you hand out so that you can figure out what it is you/client actually want. I don't think of those as first drafts though. Maybe it's a language barrier thing for me.
"Design" has a spectrum of level of detail, anything from a whiteboard full of information to a description of code in a fancy tool that is more detailed than the code itself.
Text (source code) as a representation of ideas can be worked on extremely efficiently at arbitrary detail. At low level of detail only beaten by a whiteboard.
If any piece of information has been missed when creating anything (any form of design or code), updating mutiple implementations of the same thing takes more effort than updating only one (the code).
Too many details in design will require frequent changes, with low level of detail it won't help much to detect missing pieces of the puzzle. Either way it adds effort.
Design has its advantages, lower total cost/effort in the short term isn't one though.
First draft could mean a lot of things. If you mean something you write then rewrite before it's ever released, the same still kinda applies. You might be mid implementation when something changes and ruins whatever structure you had. Or maybe the abstractions aren't very obvious at first even if nothing is changing.