So, as I forgot to say, I agree with your solution to the issue as long as prices fall to global averages as well as salaries.
It will equalize globally. Places with low salaries and low cost of living will see both rise. Places with high salaries and high cost of living will see both fall. Standards of living will also equalize, which probably means those who currently have the highest standards will see theirs decline, though not nearly as much as the low standards of living will rise.
This has already happened quite a bit in India, and in China. Labor costs have risen substantially, and cost of living has increased, too. For that matter, the cost of many types of goods has fallen dramatically in the US. Basically anything that can be manufactured overseas and imported is significantly cheaper than it would be otherwise. Clothing, for example, costs less than half what it did, on an inflation-adjusted basis, than it did 30 years ago. Toys, electronics, also dramatically cheaper. In fact, strangely enough, most of those things are actually cheaper to buy in the US than they are to buy in the places they're made!
Note that this equalization won't happen instantly, or painlessly, and there will be winners and losers in the short term. But it's the right thing.