What makes for a good index in this scenario?
Ronaldo's comment got me thinking and the more I think about it, I would answer my own question as: if every row of a table needs to be read, then there is no way to order the way that data is stored in order to improve the read performance. In other words, there's no index that would make the update statement in my scenario any faster because every row needs to be read to be updated in that query (regardless of the fact that the query has a filter because the filter doesn't actually return any less rows than everything in the table.)