One of the big problems with overseas production of most consumer products is shipping. That's why P&G has focused on regional plants worldwide for years. They could have been bringing cheaper labor soap from overseas for years, but they haven't been.
A case of any of this stuff weighs a lot (roughly 8 lbs/gal) and the profit margin isn't that great. You'd have to freighter it from China to the US.
Tankers come in all sizes. Shore tanks are plentiful. The Houston ship channel could be the bottling point for your next jug of Tide.