Why do you think Wordsworth has chosen the song of nightingale and the cuckoo in comparison with the solitary reaper's song?
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.
Wordsworth was a nature poet and nature lover, who found God's presence in nature. Also, as described in his long autobiographical poem, The Prelude, and in his introduction to Lyrical Ballads, he believed part of his calling as a poet was to present common laboring people, usually looked down upon and despised at that time as rustics, clowns, or simpletons, in ways that would show their innate dignity and worth. He romanticized them. He had been quite taken as a young man with the ideals of the French Revolution, with its emphasis on the brotherhood and equality of all men, and while in France he was deeply disillusioned by the violent turn it took. Yet he felt profoundly that the common person could be portrayed in a positive light.
By likening the solitary reaper to a nightingale and a cuckoo he is showing her as a beautiful natural object. She is not simply a laboring drudge but through her sad and "plaintive" song as she works becomes a sublime being with the power to move a listener's soul.