EDIT: Now that I'm somewhat more well-rested, I see that I misinterpreted the purpose of this thread in my original response (as noted by Jim). Plowing ahead, nonetheless:
I may be implementing my simpler approach for the SatoshiRoller app (using cipher streams).
It would be only of limited use. Bitcoin Wallet updates the blockchain in the background, while the app is not "running". It would need to ask for a passphrase just for that.
Yes, it's true that to even launch the app (to sync block chain and see balance), the user would have to supply the passphrase. That's where Jim's implementation will be much more capable (only requiring passphrase for private key operations). For a high-security environment, you'd want the passphrase/cypher_key to be wiped from memory as soon as possible. For a medium-security environment, the passphrase/cyper_key could be entered at startup, then remain in memory for the duration of the session. No-passphrase operation could be offered to users for low-security applications.
If you have an encrypted wallet and all your backups are encrypted as well, including encrypted paper backups -- you have a brain-wallet. Not exactly a brain-wallet, just all the downsides of brain-wallets. You are at significant risk of losing your coins no matter how good you think you are. Either because you forget your encryption passphrase because you only used it once five years earlier when you made the backup, or because you get hit by a bus and take the passphrase (and BTC) to your grave with you. If the encryption is implemented properly, the backup will be useless without the passphrase.
I have no problem with having encrypted backups in addition to an unencrypted backup stored somewhere secure such as a safe or safe-deposit box. But I think if the option is there, a lot of users will make 100% of their backups encrypted, and a lot of BTC will be permanently lost.
Along with the above statement, this decision is based more on the nature of your expected user base. If you target tech-savvy users, then they can be offered more options and be expected to understand the ramifications of their decisions. If the intended audience is non-technical end-users, then reliability/recovery might be most important. I suspect that Armory is the former.