[enneff]

For Chrome Sync data, you can specify a pass phrase that is not your Google Account password, nor is it tied to a specific device. It would be nice if you could specify a pass phrase to use when sending Android backup data.

Of course, many people would set the pass phrase when they set up their phone and promptly forget it, making their backup useless. (I've done forgotten enough crypto keys myself to know...)

Like you say, it's a tradeoff, but the Chrome team has been able to make it work with Chrome Sync. Of course, you only need to set up Sync once, and if you forget your Sync pass phrase you're not losing much. Perhaps the Android team decided that pass-phrase-encrypting the backups would cause more problems than it might solve.

nb: I am a Google employee, but I have no inside knowledge of any of these products nor the decision making processes of their teams.