If they don't, P & G will.
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.