Do I need to install a fuse on a altenator wire?

Never seen that happen, and cant imagine it, but.............. never say never I guess. Headers rattling on stuff used to be common in out A-bodies; there is only so much room under there, and it all wants to occupy the same real-estate when goes past the bellhousing. I've even jammed a chunk of 2x4 in there in a temporary pinch.
Another thing a strap like that can be used for is to support the exhaust after you unbolt it from the collector.

My only thought on the strap is that it makes the engine-exhaust too ridged, so any flexing as the engine rocks will cause the headers to crack faster, since they would take the brunt of the flexing.