Deleted scenes in the FFC canon are very critical, and IMHO a lot of things that were cut out of the Godfather movies should have stayed in, and my guess is the studio made him cut scenes for the sake of shortening these relatively long movies.

How important? See Apocalype Now Redux which includes several deleted scenes, including an entire section devoted to a post colonial French family living in the jungle and refusing to leave. There is no question that this version, released by FFC a few years ago is far superior to the original.

BTW note that in Apocalypse Now FFC used some of the same actors he used in the GF films including Brando, Duvall and
the guy who played Sen. Geary (he was a General).