I am speaking of the Popes pushing their primacy, etc. from 800 A.D. on......starting with the issue concerning St. Photius.
When there is a reunification, — in 100 years or 1000 years, — obviously, both sides will have to come to common terms on the papacy, the Creed, and maybe original sin, but there is no desire at this point on the part of the Western Church to influence any doctrines, liturgy or practices in the East. Rome is VERY comfortable with multiplicity of rites, local disciplines, local pieties, and compatible local doctrines, such as Hesychast.