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My understanding is that, in large part, it's because the compactification by stable curves/maps can be fairly easily constructed with GIT, and have been studied before. Most of the results people actually really want to have involve showing that the class of curves in something is actually contained in the locus of smooth curves (which really is the case for rational marked curves). The intro article by Fulton and Pandharipande discusses this a bit, in the case of homogeneous varieties.