Or maybe there's a simpler answer; having Patrick Mahomes on a rookie QB deal gave the Chiefs a really great roster for a short window. Much like having Russell Wilson on a rookie QB deal led to some all time great rosters.
Aaron Rodgers was playing for a $6.5m cap hit the only year he won the Super Bowl. Big Ben was on a rookie deal in Super Bowl XL (4.2m). Joe Flacco was playing on his rookie deal when he won one with the Ravens. Doug Peterson had two cheap QBs with the Eagles. There may be other factors that are worth discussing in all of those situations, but 'good QB on a cheap deal' is such a dominant advantage in the NFL that's it's difficult to fairly evaluate other factors.
Aaron Rodgers was playing for a $6.5m cap hit the only year he won the Super Bowl. Big Ben was on a rookie deal in Super Bowl XL (4.2m). Joe Flacco was playing on his rookie deal when he won one with the Ravens. Doug Peterson had two cheap QBs with the Eagles. There may be other factors that are worth discussing in all of those situations, but 'good QB on a cheap deal' is such a dominant advantage in the NFL that's it's difficult to fairly evaluate other factors.