I think that part of the reason for the comparison might be to emphasize the uniqueness of the song. The nightingale and the cuckoo birds are rare. They are not birds to be seen in an every day context. They are not abundant in nature. When one sees them, it is a rare experience, one that has to be treasured. In much the same way, the solitary reaper's song is a rarity that compels the speaker of the poem, presumably Wordsworth, to be stopped with a sense of the immediate. Just as witnessing the nightingale and the cuckoo, he knows that he is in the presence of something unique when he hears the nightingale's song.
Another rationale for the comparison might be to accentuate the sound qualities of the song. Wordsworth's challenge in the poem is how to convey the beauty of a song without actually being able to have the reader hear it. In order to overcome this challenge, he employs the comparison with the nightingale and the cuckoo. The reader can envision the sonorous and aesthetic quality to these birds' songs and immediately connect it to the solitary reaper's song. It is in this light where the comparison becomes valid and meaningful.