I would also say it is Improbably and highly unlikely but unity, even in small ways, is something I think all Christians should strive for. This is one of my problems when thinking of becoming Orthodox myself, or even, on some days, calling myself a Christian at all. I do agree with you that the majority of Churches have very main, and commonality with each other as far as Theology goes, there are of course major differences, and just like any family we have to work through our differences and problems which takes time.
Having said all that, I think that wanting all Christians to be able to participate fully with each other is a desire of God, and because we are made in His image it is only right that many of us should also have that desire. I would pray and ask guidance from the saints, the Holy Theotokos, and our Lord Christ Jesus for how to rightly, and best to go about becoming more unified and how we should fulfill God's desires in our own lives first before looking towards unifying everyone else...I hope that makes sense. May Peace be bestowed upon you.