The reason I had to replace the OEM backbox on mine was that the box had rusted through under this strap.
I replaced with a Daytona SS system which came with a Stainless strap, so won't have that problem again.
As to what the strap actually does?
The back box is supported on two hangers anyway, so I suspect it's more to stabilise the cat/ downpipe, and the joint between them as Clive says.