on Eucharist

What role does the Eucharist play in the life of the Church?

It seems that the many churches that enact closed communion believe that communion is a sign of church unity. Christians who attend other churches are not able to partake in the Eucharist in this situation because they are not considered to be in union with the church that is providing it. I know there are also reasons having to do with individual purity and such concerns (Paul goes into these in 1 Corinthians), but to be honest, this doesn't seem like a convincing argument unless you are willing to say that members of your church have attained that height of purity and that in restricting communion to them alone, you are in a sense protecting others from their own impurity. This seems arrogant to me...but maybe I'm muddled on this.

What interests me, though, is the church unity argument. If I grant that the Lord's Supper is integral to church unity (as I believe that it is), I still struggle with the actual role that it plays. The closed communion position seems to see it as a sign of unity. But I wonder if the Eucharist is actually the source of our unity. If it is actually partaking of Christ's body and thusly becoming one with him and the righteousness of God (God's covenant faithfulness) and our own resurrection in his glory, then the Eucharist is more than the simple outworking of the church's unity. It is in the eating that the church is unified.