I like the big aria from La Cenerentola, and I liked hearing Juan Diego Florez sing it, but it isn't very suitable in Barber. When Rossini wrote it, it was for an opera called Almaviva. Same opera, different name. There it would make sense. Figaro is almost a bit player in this version.
In La Cenerentola Angiolina has just become a Princess and has more than enough reasons to celebrate. The opera would seem unbalanced without it.