Crop picking (in some cases) takes skill and attention to detail that lawn mowing mostly doesn't. Some crops, like tomatoes, are very easily damaged if the picker isn't religiously careful. I think it's more in line with the other jobs in being not worth what employers want to pay for enough Americans to satisfy demand.

Another possibility, though, is that lawn mowing has no giant corporations, and hence no industry-wide employer lobby to push for visa programs.