It seems like there may be a market there.

Every 10 to 15 years, you send in your archived (and new/interim) personal data and get it back on the current top-tech storage medium. That way it's not stored in the cloud and you can keep moving the stored data forward without having to deal with it all yourself.

Not really. You can buy a 18TB hard drive now. Even if your data is humongous and needs several of those, it will likely fit on a single drive in 5-10y. So it takes an increasingly smaller amount of time to replicate (excluding the copying time which keeps the machine busy but not you).