> The company would pay corporation tax in Ireland.

You'd assume that, but you could also very well be wrong. Depending on tax treaties and the "effective place of management" principle, he could be liable for corporation tax in Spain or in both Spain and Ireland.

One reason why tax laws get very complicated very fast is because every country wants to tax everything it can which inevitably means that two different countries end up taxing the same thing. To avoid this, you get double taxation treaties and loopholes.

In the example above the American company presumably has most of its employees in the US and ought to pay significant tax there somehow.

It will: the process of paying employees is heavily taxed. Who writes the check and what the nominal salary is doesn't matter too much... between the cost to the company, and the employee getting to spend the money, the government gets what 30-40%? That's a lot. And it's hard to avoid, you can't move a hundred engineers to the Bahamas at the stroke of a pen.