When to Partake: Or The Lord's Supper and the Gift of Objectivity

Lately I've been reflecting on a phenomenon that's consistently been a part of the church settings in which I've been involved.  At times, though I don't know if it's most of the time, the pastor leading the congregation in the celebration of the Lord's Supper, once the elements have been distributed, will give us the chance to partake "in our own time."  In other words, the people are expected to have a time of individual (and silent) confession and prayer and, when each is ready, they eat the bread and drink the cup on their own with a worship song in the background.  

My question is this: do we lose something when we do things this way?  In light of Paul's discussion of the Lord's Supper in 1 Corinthians, I wouldn't say that individual examination is out of place.  Even so, I've begun to think that we do risk missing something here.  Most of us journey through the week operating in a sort of self-contained spirituality.  We have to engineer the content and structure for our devotional practices and we have to work at reminding ourselves of the gospel.  Perhaps partaking simultaneously with others as the minister instructs us, guides us, reiterates the gospel 1) releases us from having always to contrive an individualized approach to God (this is church, after all!), 2) more readily catches us up in the grander narrative of the church in redemptive history, 3) mercifully reminds us that the gospel comes from without and doesn't depend upon our ability to develop in the moment a manageable way to connect ourselves with God.  (Though I've lived and moved in churches of a Baptist orientation, this line of thinking reflects a desire somehow to appropriate the Reformed insistence on the sacraments as signs and seals of the covenant, divine confirmations from without meant to strengthen our faith.)  

Any thoughts on this?