I understand part of the reasoning for minimal clearance between the casing and the fan blades, is to have the larger fan blade possible, which generates a larger low pressure area to increase air intake.
However I don't understand why, if leaking occurred, it would reduce the overall efficiency.
If it was to leak, it's still going through the intake to the compressor or bypass duct.
If it was to leak, it's still going through the intake to the compressor or bypass duct.
This is incorrect. A "leak" would cause the compressed air to circle around the fan and exit again from the front, reducing the efficiency of the fan, because part of the power would be used to compress air that does not do any useful work in the engine.
The circling around is a consequence of the work the fan itself does: after the fan the air is at a higher pressure than the air in front of the fan, this means that the air outside is pushed back by the air inside, and if there is a leak, the higher pressure air (inside) leaks out from the front.
Minimizing this "leak" helps maximising the efficiency of the fan, and of the engine as a consequence.
It would result in vortices forming at the blade tips, generating drag. Those vortices are the same that come off of the wingtips of airplanes and the blade tips of helicopters. Aircraft manufacturers have made winglets pretty much standard to minimize this drag, and not allowing the blade tips to give off those vortices (by putting them very close to the engine nacelle) will increase efficiency just like winglets do on a wing.
