With respect, it ain't that simple. Because error correction means keeping around the data that defines "without error", and that data is subject to the degradations of time, too. One cosmic ray going through your data store, and you no longer have pristine data.
So you keep a backup of your backup, right? And when cosmic rays go through both the original and the copy at different points, which copy do you trust? You technically need to keep a number of backups so large that the probability of bit-rot over enough of them becomes vanishingly small over the expected lifespan of the structure.
And then, you need to have an energy source that lasts as long as well - correcting errors and making repairs cost energy.
Overall, the laws of thermodynamics amount to: You cannot win, you cannot break even, and you cannot quite the game.