it makes more sense to me to be silly about "personal continuation" in this direction than in the non-uploading one that's far more common. Which is not saying much really.

I don't put any value to something being "the same" over time, but apparently most humans do, especially when it comes to people. If someone does care about someone's continuity in a way that follows the assumptions listed in my post, then logically they should derive value from the procedure described.