They are all from a separate game, so they don’t much about each other canonly. But in the Ultimate talent development plan, Ibuki knows them both because of their musical talents.
Ibuki greets Kaede and Sayaka, Ibuki also compliments Sayaka’s smile. Like before, Ibuki knows the two because of their musical talent. Sayaka says she was thinking of a collaboration with Kaede and Ibuki. Sayaka desired making a music video with Ibuki or sing a concert with Kaede. Kaede thought it was a good idea that they should share their interest in music. They all agree on a collab and Sayaka worries about the collab, but Kaede assures Sayaka it’ll be okay.
The three all share different kinds of music. Ibuki does loud music and make unnecessary noises, while Kaede just does piano and no singing. And Sayaka does singing and dancing, but it’s different from Ibuki’s loud music. However, Ibuki and Sayaka both do singing and Sayaka and Kaede both play an instrument.
Sayaka, Ibuki and Kaede’s personality are shown to be somewhat alike, they also have some things in common. They’ve been shown to be cheerful students. Ibuki and Sayaka are wearing what appears to be a school uniform/sailor uniform. Ibuki is shown to have plenty of pink on her, so is Kaede. Both Sayaka and Ibuki have been murdered in the killing game. Kaede and Ibuki are beloved characters. Despite all this, they all are shown to enjoy their musical hobby.
The ship sailed due to the three sharing a common interest and each being the token "music girl" from their respective games. The fact that each person is from a different one of the three mainline games is kind of an attractive point of the ship. Since the three are known to be students who enjoy playing music and that their talents are based on their musical hobby, people find that somewhat interesting. Some think about what they might do if they had a band or musical group together.
Since they seem to have similar personalities and mindsets, it is believed that the three of them would get along very well. Additionally, their colour schemes mainly stay within the range of only blues, pinks and whites, it can be seen as an aesthetically pleasing group.
As the three have only ever met in Ultimate Talent Development Plan, and not in the main games, the ship is considered a rarepair. Even without UTDP, it may have had supporters as the three share an important part of their characters with each other. With their interaction in UTDP, it opened the ship up to those who might not have considered it before due to them never meeting.