Ryan,
Members notice when maintenance staff cut into the fringe - ugly mowing pattern, scalped turf, discoloured grass. Therefore, maintenance staff will err on the side of caution if they can't make a perfect pass.
If left unchecked, losing for example, a mere 1/2" per year around the perimeter of the green can greatly reduce the overall putting surface. Using a 6,000 sq. ft. circular green built in 1920 as an example, you can see how quickly it looses surface area (approx. 11 1/2 sq.ft. per year);
1920 = 6,000
1950 = 5,663
1980 = 5,335
2010 = 5,016
If the green in question was originally more square, as many classic designers intended, even greater loss would occur due to the triplex mowing issues mentioned above, resulting in lost corner hole locations.
TK