I attended that game. Another factor was the Bear had preferred smaller and quicker linemen during his first decade or so at Alabama. Sam Cunningham was as big as many of Alabama's linemen and linebackers, which made bringing him down even more difficult. He changed his philosophy about the size of lineman during those same years.
IIRC in 1971 he introduced the Wishbone, and that’s what led to their success in the 70s.