In addition to the benefits you mentioned, it shortens the testing and acceptance phases if you finish things as you go. Instead of saving all the testing and feedback till the end of the cycle when you really don’t have any time do do it right, if we finish features, get them tested, and get feedback, then when we finish the last one, we are done.

Traditionally, we get everything "finished" and then there is a long testing and debugging cycle.

This is implicit in your post, but I thought it might be helpful for it to be explicit.