"Now you'd think...really...that it would make sense to delete the files first, then do the backup?"
I would say that that would absolutely make no sense at all, and I thank MS on my bare knees (as a manner of speaking
that they agree with me. It would be very bad to delete the previous backup unless you were 100% sure that the new backup was OK (that is: written to disk and preferably verified too). Otherwise if the backup failed it would be possible to end up without a valid backup since the older one was already deleted.
I think that if you choose to keep 2 old backups, you should know that you are guaranteed to have those, even if the last backup failed for some reason. In your scenario, if a backup failed, the older one would already have been deleted. Backups are just to important to take such gambles with!