The arc can represent anything we wish. Pre-Christian religions, for example, represented a mystic palm tree with a simple arc, and this symbolised fertility.
Another interpretation of the hoop is as a capital Omega, meaning everlasting life.
To enshrine simply means to encase or to put in a reliquary (shrine is from the Old English scrin: 'a box for relics'). The act of enshrining something doesn't make that object more holy; it is just showing that we acknowledge it is holy.
Sometimes the enshrinement is incidental, where the main function of the covering is to protect the cross from the weather. (See Wayside Cross)
As any shop window dresser knows, drawing a box around something gives more visual focus to that thing. Enshrining a cross brings focus to the cross.