While you may be right about the current use we have for DNA, it's very likely that medicine will have many more uses for it in the future. Prices on genome sampling are going down rapidly too, so it's reasonable to use this as an example why we might want to store data error free for at least a century.
There will be many more things we want to store. Remember all those old city records and paper books? The news paper archives? early 20th century cellulose film? All those data sources have their problems and we have already lost a lot of information that is valuable to us now. Your parents and grand parents color photographs have lost a lot of the color in them already. Not just the prints, but also the negatives. Those VHS video tapes of your dad growing up? They're turning into noisy images right now.
People have plenty of reasons to come up with a proper way to store data in such a way that it's still accessible for future generations, or themselves later in life.