A DMCA takedown request doesn't prevent you from distributing your work. It informs somebody else that continuing to distribute your work is legally risky, and the somebody else has to decide whether to take your stuff down or face possible liability.
By this definition nobody distributes their copyrighted work themselves: editors, printing companies and transporters do it for book authors, music companies, cd printing plants and transporters do it for musicians, etc. So by your definition it's essentially impossible to interfere with the author's exclusive distribution right. That's nonsensical.