When a cell is denucleated, either naturally as in red corpuscles, or in the lab, the cell does fine until it sustain some damage and needs repairs. Then it dies because it has lost the blueprints. Making proteins is not necessary once they are made and the cell is mature.
They are not a valid example of how a cell can function without DNA. Their only function is to float around and have stuff stuck to them. Other cells actually have to produce proteins and such.
At least, that's how I think it works. Are there any cells (other than red blood cells) that can actually "function" (do things, not just have things done to them) without DNA?