A medieval development in church design was the rood screen. It is a semi-transparent barrier between the nave and the chancel. At the top would have been a Crucifix, hence the name 'rood screen,' for rood is a derivative of the Anglo-Saxon word for cross. A 15th century French example can be seen in this picture.
The practical purpose for rood screens is to fulfill the Fourth Lateran Council's decree that the clergy explicitly act to protect the Blessed Sacrament from abuse or easy access, as it is around this time that the Sacred Host is reserved for long periods in the tabernacle, coinciding with the development of transubstantiation and the practice of Adoration.
There seems to have been certain ritual usage for the rood loft in the more important collegiate, monastic, and cathedral churches for the singing of the Gospel, although not in the parish churches, since the Sarum Use (I know, not the exclusive form of the Mass in England but influential enough) is very elaborate, space-permitting. Even its ritual usage is hotly debated. Firstly, the rood screens were destroyed by the Protestant revolters in England, meaning it's hard to figure out how it could be used, and the texts for the liturgy were slightly ambiguous.
The Council of Trent desired that certain barriers be removed from the churches, so that the liturgy might become more accessible to the faithful. However, Trent didn't explicitly call for the removal of rood screens.
Sounds familiar to the modern ear...except for a few major reasons which distinguish the two.
Altar rails were by and large ripped out after Vatican II for a variety of reasons, which often add up to, "because, reasons," since they have little theological backing in light of the 2000-year tradition of the Church.
The rails have been used since the era of the Church Fathers, and serve a clear purpose to delineate the area between the clergy offering the sacrifice, along with their ministers, and the laity. They have a practical function, which allows us to easily kneel for Holy Communion. The Communion cloth- another ancient practice- can be attached to the rail permanently and simply unfolded during Mass.
Rood screens are a late development when compared to the rail, and the Church should back-track on items which might be nice, but are inessential or ultimately a hindrance to liturgy. Also, their liturgical function seems to be limited to the Sarum Use, and since that was wiped out for the most part by the Protestant schism, there remains no need for a visual barrier except in certain monasteries and convents.
Cardinal Arinze's offer of a turkey for those who can find the place in the Constitution on the Liturgy from the 2nd Vatican Council where it orders the removal of the altar rails still stands, but I think it will stand for all time.