(Abu Hurairah narrated that: The Messenger of Allah said: "There are two joys for the fasting person: the joy when he breaks his fast, and the joy of when he meets his Lord.")

[Bukhari]

What brings the joy to the one who breaks his Siyaam? Is it that he is over with the commitment of Siyaam? No, it is not.
Siyaam is loveable, but the one who fasts is joyful, because Allah the Almighty helps him observe this act of worship. He is joyful, because Allah the Almighty dignifies him with being able to offer prayers during Ramadan in the Masjid.
The first thing, Eid in Islam comes after major acts of worship, and the joy on Eid manifests the happiness of offering this act of worship, given gratitude comes after bestowal.