No. It wouldn't and it rarely does. EC 261/2004 is for involuntary downgrades. By definition, these are not involuntary.

So, why take less than EC 261/2004 provides? Because that may go to someone else. Volunteers provide a win-win-win. The carrier deals with a problem at lower cost, a pax who might have been DG against their will isn't and someone who is fine with a flight in a lesser cabin gets something for his troubles.