The amount of energy required to rotate a blade is going to be related to the moment of the blade (mass times distance^2, approx) and the resistance to the blade as it moves in rotation. If the grass is a consistent density along the length of the blade in rotation, and the blade is honed to a constant sharpness, then the greatest transference of energy is at the blade tip and decreases as the square of the moment arm.

In other words, a blade does more work at the tip than anywhere else. Thus, at length r, the work done will be proportional to torque at r^2 X rotational velocity. Since torque is related to the moment arm length, every unit of decrease in length (n) will see a decrease in work related to (r-n)^2. As n approaches r, work goes to zero.

Thus, the metal at or near the axis of rotation is nearly incapable of doing work, regardless of how sharp. In fact, it is more effective to have the blade sort of hump-up near the axis of rotation so that the metal wont be a frictional drag as the mower goes through rectilinear translation.

Finally, if one were to sharpen the blade from tip to axle, and run fast enough to make cutting at the axle possible, it is more likely that you would stop the rotation than cut the grass. This is why shaft locks are put on the shaft, not on the moment arm.

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