Actually, the peeve is that capital (and profit) is now permitted to be mobile, while labor is generally not. The EU trade zone is the one, shining notable exception.
That is: we move our money into whatever markets we want, we withdraw our profits as we choose, but heaven forbid that labor should be allowed to move as it pleases.
> Pitting one workforce against another is an old trick used to control them all.
It's not a trick, it's the same as you choosing the cheapest product on a shelf between two competing brands. It's the foundation of a competitive market that puts high incentives to produce products the most efficiently and most cost effectively. Which is a huge boon to consumers and has lead to us all having a better standard of living than anyone else in history.
Being in country A and able to choose products made in country B is the result of specific political and legal choices made by the power structures of both countries.
Historically, there was nothing inevitable about the free movement of capital, goods and profit, but over the last half century or more, this has come to be seen as "normal".
Your argument is the classic one in favor of removing restrictions on the movement of capital, goods and profit (not labor!), and has been the justification for almost every free trade agreement over the last 75 years.
The evidence of it being a net benefit to everyone is now starting to skew against that claim. The distribution of negative environmental externalities to poor countries in particular argues against it (i.e. country X can make your widgets cheaper because they have less regulation about waste and pollution).
We're all consumers, it is true. But we're all citizens and employees too, and we spend more of our lives in those roles. Global free trade may be a boon to our lives as consumers, but it's been fucking over our lives as citizens and employees for too long alread.
Either allow labor to always move as freely (or a un-freely) as capital & profit, or move back towards less international trade, certainly between countries with highly disparate income levels and legal systems.
I would posit that it is more akin to exploitation to keep rich nations rich and poor nations poor.