I'm not sure why this has created an argument but gen 0 was started by 1st holofes. Every gen got a group song, so in order to make things fair they grouped the solo talents together and gave them a group song of their own to perform (Dream Story). Afterwards the solo talents warmed up to the idea of having their own gen (it was also popular with the fans), so they stuck with it.
Any comparisons to gen 2 are irrelevant, gen 0 is an ad hoc group made out of convenience, but that does not delegitimize them. Unlike gens 1 through 5, gen 0 is still entirely intact nearly 5 years after they were founded. Their ability to stand on their own makes them resilient and they still come together when it matters.
Footage of gen 0 coming together for an important occasion:
https://www.youtube.com/watch?v=wP8yUHvnKrI 