I wouldn’t say it’s a false sense of Mysticism. You don’t see any Eastern Catholic schools or hospitals either. Eastern Catholics approach the faith the same way the Orthodox do, and we wouldn’t dismiss the Eastern Catholic approach to spirituality as being “less Catholic” or fake.
And when the pope speaks, the west listens. Conversely when the Moscow Patriarch or Ecumenical Patriarch speaks, the East listens. I’m sure clergy in both communions follow what the leadership of the “other side” speaks, but I know many Orthodox (including here in the United States) who don’t follow Catholic leadership at all. And it’s not out of some anti-catholic zeal, it’s just that the Pope has no direct bearing on their day-to-day life a a Christian. To be honest, this has been my experience in Eastern Catholicism as well. We pray for Pope Francis at every Divine Liturgy, but beyond that we don’t really focus on Rome at all. There’s no need to. The Bishop of Rome when not speaking magisterially to the entire Church is only operating as the Bishop of Rome and as such, is limited to the Roman See. The Roman Church certainly gives the day to day of the Pope’s business more interest than it needs to, and this isn’t a bad thing. But in the sake of fairly representing Orthodoxy, I wanted to give my input. Thanks!