You bring up a good point that the Design Specification document would be a great tool for the vendor.
Some companies prefer to forgo the whole design specification process and choose, instead, to have the vendor design a prototype from a general description of what is required and work from there. Sort of like the old adage "A picture is worth a thousand words."
Perhaps the best method would be the one that is quicker and cheaper; without sacrificing quality, of course.
Have you ever been involved in online course design?
Jane