... It showed a human side of Michael.
There were plenty of scenes showing 'a human side of Michael' that remained in the film(s). People seem to focus more on other things, though.
Anyway, there was once a thread where people were asked to name some of their 'favorite' deleted scenes, and/or those they wished had not ended up deleted.
Mine was that of Bonasera preparing to meet with Vito at his request following Sonny's death. Absolutely dreading what Don Corleone is about to request of him and cursing the day his wife and Mrs. Corleone became friends...