>If "the cable rating is a lot less than the fuse", then what would be the point of having a fuse in the circuit?
Good question. Two separate answers:-
. Jimmy's bike is unusual, in that whoever did the wiring made several mistakes - mixing up fuse 'blow' and 'continuous' ratings was one, using too-thin and -low-rated wire was another; if the fuse had been 15A and the melted wires 17.5A or 25A 28-strand, the fuse would've blown before the wires got hot enough to melt the insulation. The worst Jimmy would be dealing with was a blown fuse.
. Whether we like it or not, standard Britbike wiring was designed and evolved for years by BSA's accountants, not by BSA's or Lucas's electrical engineers. If we're rewiring, many improvement aren't expensive but the person doing the rewiring has to know what needs improving.