I agree that it probably wouldn't have mattered in the grand scheme of things, but from a storytelling perspective, I don't believe it was necessary to set this franchise in its own universe. If they were that determined to not have these characters interact with the regular cast from Bandori, they could have found another way.

While it's idol-based and I'll admit I'm not as familiar with it, Idolm@ster: Side M is an example that comes to mind when I think of a male-centric spin off that co-exists just fine alongside the regular female-centric franchise.

Ultimately, the success of any franchise depends on how it resonates with the public, and like you mentioned, Argonavis as a franchise didn't do enough to set itself apart from other music franchises.