If a bigger fan increases fuel efficiency is taken to its logical conclusion, soon the fans will be so big as they will be hard to hang under wings without scraping the ground. Would it therefore be beneficial and fuel efficient to add more engines with higher bypass ratios so as to shift more air? Example: instead of having 2x engines rated at 10kN (in the core turbine, I'm not talking total thurst from the fan part) each and with a 100sq.ft fan area - would it be more beneficial to have 4x 5kN engines with 200 sq.ft fan in instead?
This is a reason why Airbus built A340-500/600 rather than A330-500/600.