Osipova is wisely using her opportunities at ABT to learn new roles that the Bolshoi has not cast her in. Everyone already knew she would do a great Kitri. Now she is showing the world what she can do with roles that she has not done with the Bolshoi, like Juliet and Aurora. Had she ever performed Giselle or Sylphide before her ABT performances last year?
Yes, with the Bolshoi. I think we cannot say at all that she is underused in her home company: she is dancing almost everything of new and old they are staging (Esmeralda and Coppelia among the latest new things).
Anyway, good for her to have also opportunities elsewhere (it's funny that in few days we will have in La Scala another Bolshoi debut in MacMillan Romeo and Juliet: Volchkov as Romeo... maybe time to have the work in Bolshoi repertoire?).
I think Osipova made her debut as Nikiya in Novosibirsk before dancing it at the Bolshoi (I feel that Aurora should suit her better than the Bayadere).
There are a few cases of dancers making a debut in another company: Cojocaru, for example, made her debut in La Sylphide on Bolshoi stage.