One of the reasons Dropbox is successful is because anyone can use it. Even your mother. In fact, one of the reasons Drew was originally accepted into the YC program was because his sister was using it when he applied.

"If I can look at my data any time I want, I just need the key to it. Dropbox just gives me access to the encrypted stream."

In order for the data to be encrypted securely, you would need to generate a key on your own computer which Dropbox then uses to perform the encryption. (Tarsnap works this way.)

Forcing Drew's sister (or your mother) to generate a key would be bad for accessibility.