The purposes for large perimeter cames are several.
Easy adjustment on site. It is often the case that windows are not totally regular in their dimensions, even though you have taken the measurements carefully. Variations in width and height can be accommodated by shaving the lead in appropriate places. This avoids having to take the panel back to the studio to reduce the size of the glass and put new perimeter came on the panel.
The width of the rebate has an effect on the width of the came to be used. The wider the rebate, the wider came you will want to use. The minimum width of came you want to use with a 10mm wide rebate is 10mm came. This will give a maximum of 2.5 mm of came showing if you have a glazing allowance of 5mm. Often 12 mm came is better. In general the came should be wider than the rebate is, but not so wide that the heart of the lead is outside the rebate. In church windows, where the panels are installed into the stone, the cames are frequently 16mm or 25mm wide to accommodate the variations in width and the flexibility needed to get the panels into the slots.
Aesthetics have an effect on the width of the perimeter came too. Various people want more or less came showing. The important limitation is that the heart of the lead should be within the rebate.
In autonomous panels the need for large edge cames is to act as a framing device. Zinc might be used but there are other possibilities than using a different metal that will provide as good or better solutions.