What is more complicated in the EU generally than if you were in the US? And is EU law the issue or really 'local law'?

For example, you mention tax. An affiliate is a cost to you and in principle you account for that cost in the same way whether that affiliate is next door or on the other side of the world.

There's also potentially VAT. My understanding is that VAT treatment of services received from EU and non-EU service providers is the same. If so there should be no added complexity.

In any case, this is quite a technical topic and if you want to understand your position and your options you should really hire a professional knowledgeable in that very topic.