Would you support a law that requires manufacturers to put the COGS of their merchandise on the label?

No. 

Cost Of Goods Sold is irrelevant to most buyers and is a commercial secret for manufacturers.

If you want to avoid buying exploitative goods manufactured using underpaid labour or even child labour then just look for goods marked up as Fair Trade or many other similar schemes. Don’t buy from outlets infamous for having been found repeatedly to have done that such as TK Maxx and others. 

Your dollars = your choice. 

Your choice = your responsibility.