As always when it comes to cheap goods, we have ended up in an argument about labor. This is not surprising. One of the prize achievements of the left was creating something close to a labor cartel that could extract rents from other citizens--something I'm sure you'd categorize as workers organizing to demand their "fair share". Globalization has indisputably upset the cartel.
While you attribute a heavy role to the consumer in all of this, I don't see much in economic history to bear you out. Consumer outrage over its fire safety violations did not put the Triangle Shirtwaist Factory out of business; the fire did. The various changes that followed in labor practices did not come about because consumers were outraged by the way their clothes were made. They were accomplished through the heavy hand of the state.
Whether or not you think these were a good idea (I'm a big fan of the fire code, not so much of special laws for women workers), they were not undertaken because Americans desired them in their role as consumers. They happened because Americans were outraged in their role of voters at what had happened to fellow American citizens. They used their power as voters to allay their outrage by changing work rules. But in a modern economy, it is simply not possible to monitor the conditions under which all the goods we consume are made. Perhaps some sort of auditing organization could be created, but then you have substantial interpretation questions--witness the endless wrangling over whether various nationalities of garment factories constitute "sweatshops". But even if it existed, most consumers would ignore it. Look at the paltry success of the Made in the USA labels--and they have a deep atavistic tribal instinct on their side!
The anti-globalization left's problem with cheap foreign goods is precisely that we can't extend the power of our state over there, to enforce our labor rules. This threatens the power of our labor cartel here. To be sure, they argue, as you do, that foreign companies put pressure on local governments to counter the demands of the labor movement. This is undoubtedly true. And some of that pressure is self-serving demands from corrupt officials. But western companies also do things like demand better roads, better ports, better public transportation, a more reliable electrical grid, and less corruption in government, because those things make their factories more productive.
I am, in general, not a big fan of corporations messing with the government. But often the "pressure" decried by anti-globalization activists consists of pointing out, entirely truthfully, that productivity in the area is very low, and they can't afford to pay much higher wages. Competition between the Asian countries that make so many of our goods is brutal. In theory, labor organizers shouldn't demand so much that their industries become uncompetitive. In practice, however, as we've seen with Chrysler and GM, they can and do.
But even if we could somehow prevent Nike from ever interacting with, say, the Vietnamese government (impossible: the government there runs just about everything important, from ports to electric plants), that wouldn't mean that wages in Vietnam would suddenly skyrocket. Western tourists in Asia love to photograph the picturesque farmers in straw hats who sell vegetables out of little baskets on the side of the road, which they have carried there in quaint little shoulder yokes. But when you stop to contemplate the level of productivity that is implied when walking miles and miles to sell a few dozen cucumbers is a good way to spend your workday, your heart breaks--and it becomes clear that western interference is not the main thing keeping wages in those countries low. The reason wages in China, Vietnam, Cambodia, Thailand, and so on are so low is that there are millions of such people on the farm who would be happy to work in a garment factory or assembly plant.