I like this question, in part because many non-genealogists assume the exact opposite, i.e. that a DNA test is a complete substitute for good old-fashioned genealogy.
In my opinion, DNA testing is a very valuable tool for genealogy. It's an especially valuable tool for our mission on WikiTree: to grow a single family tree that eventually connects us all.
You don't have to agree with M's premise about the flood and Biblical ancestry to agree that we are all connected somehow. We do all have common ancestors.
It's like a puzzle. You start a puzzle knowing that all the pieces will eventually fit together. But you still have to put together the pieces.
Genealogy is about putting together the pieces. Seeing how they fit. DNA is a great tool for this.
Paper records are often inaccurate or incomplete. A DNA connection can help confirm what you suspect. It can also disprove something we assumed to be true, which then points out the need to do more research.
Moreover, DNA can be the only link in some cases of adoption, illegitimacy, etc.