But also, the free market would still allow others to fill the shoes of the companies that left.

The Free Market would also allow them to set up their business in Europe and go for that market instead. And, since they make a much bigger profit in Europe than in the US, that would be their focus. The only companies that would set up in the US are the ones that are not able to make the bigger profits available in Europe.

This is basically like the car market in the USSR after WWII. The major American, European and Japanese automakers didn't operate there, but of course that didn't mean there weren't any cars. It just meant that there weren't any good cars.