Giving New Meaning to "Handicap": The Americans with Disabilities Act and Its Uneasy Relationship with Professional Sports in PGA Tour, Inc. v. Martin

Imagine that an all-star batter for the New York Yankees had a circulatory disease that made it difficult and painful for him to run. Would Major League Baseball be forced to permit a designated base runner to run for the disabled batter starting from home plate? Consider Jim Abbott, the successful major league pitcher who was born without a right arm. Under the Americans With Disabilities Act ("ADA"), could Abbott, who pitched well for many years in the American League, which has the designated hitter rule, force the National League, which does not, to exempt him from its batting requirement?

If so, does that mean that batting is not fundamental to the game of baseball, or that allowing Abbott a designated hitter is a reasonable modification to his disability?