MS Office will always be superior to QuickOffice. QuickOffice is just an alternative. And I don't think Google can do much with QuickOffice but adding the ability to sync files with G Drive, send via Gmail, etc. Most of the products owned by Google are web-based so they will just integrate their products in it.
Ofcourse, Google has Android but users, by default, go for MS Office. And if Google tries to force users to use QuickOffice, it'll just backfire.