I say we should own them.
The problem with that approach is what we are now finding happening in China. Exports from China were almost exclusively (1) Foreign invested enterprises setting up wholly owned factories or in the early days setting up joint ventures with Chinese companies (the later very much a thing of the past now) or (2) Foreign companies finding semi-competant Chinese companies to make the goods they wanted and working with them to bring finished product to exportable standard.
The exception to this were the few stand out private Chinese companies that became successful in the new Chinese ecomonmy - Legend Computer and Little Swan home appliances being a couple of examples.
But what is happening now is that employees working at those wholly owned foreign companies have taken what they have learned and starting making products. And, those companies that learned to produce for a foreign company started looking for other business and are now actively seeking new business through direct foreign trade.
To get to your point, no one will "own" all the business places like India or China. They will find much competition from companies in those countries. And those with far more modest operating standards and no foreign investors to answer to or expat staff to pay are a real competitive challenge.
For now, the foreign companies will have a marketing and sales advantage - especially since the Chinese seem to have a habbit of pissing off their foreign customers do to cultural differences. But, that will change also.
I am convinced the only answer to save American jobs and American strength in the world and U.S. marketplace is for the government, labor unions and lawyers to stop treating American business like evil garbage for their pickings.
Despite all the recent moaning about "outsourcing" that day is not here yet. Things will get much worse and to a very sad state of affairs before people figure out what the Chinese learned: A company must first make a profit. And isn't it ironic that the concept of profit has become a dirty word in the U.S. and so seriously embraced in a communist country like China.