Mine randomly reboots semi-periodically already, even when it hasn't been shown as having downloaded an update.
That said, I think this is a fairly good idea, although with the encryption stuff they do, this will cause people who rarely use their phones to miss calls and alarms.
It would be easy to store alarms in an unencrypted partition or even EEPROM as they take no space. Calls is a harder problem, although in principle if the SIM doesn’t have a PIN, you should have everything you need.
That said, I think this is a fairly good idea, although with the encryption stuff they do, this will cause people who rarely use their phones to miss calls and alarms.