Lots of companies already audit their production chains, precisely in response of public pressure on the subject. Nike and football manufacturers are the most famous examples; also coffee, chocolate, and banana producers. This sort of thing, while not perfect, brought massive improvements in working condition in poor countries over the last 30 years.
Chocolate, coffee, and banana producers are in a different context. If you want to stop child labor on the chocolate farms, there's currently no choice but to have Nestle and Hershey do it, because the governments in Ghana and Cote D'Ivoire either can't or won't enforce their own laws on the topic.
The various Asian governments involved into tech production chains know what goes down in each and every factory. They know workers exploitation is massive, and they don’t care.