This actually makes sense -- if the goal is long-term set-it-and-forget-it, it solves the problem of getting a new credit card every few years & forgetting to change this service. It also eliminates any recurring payment-processing fees.
The back-of-the-napkin math checks out: accounting for storage, data-transfer, and business overhead, if they pay around $0.20 / GB / year, and they charge $10, then with 0 interest they would still have your files for 50 years, which is probably longer than your children will have your password to this service.
I still wouldn't trust it -- I have a pavlovian response to the combination of "permanence" and "give all your data to this new internet service". Maybe it's irrational here, but still, this product is at the wrong layer of abstraction for me personally :)