An arc approach is just another means to position to final, like a procedural (non radar) approach from the overhead.
As correctly stated above, the origin is from Airfields without Radar Equipment or as an alternative to a radar vectored approach.
I (until recently) worked at a field that had overhead approaches and an ARC/ILS approach.
The arc is particularly usefull when it is designed to cater for traffic from a particular direction. That is to say it saves the distance of going overhead the facility and then doing procedure turns then going outbound etc...
Just my opinions of course
Invictus