How do you think the tax system works?

As soon as you do business,you have to register yourself to the "tax office"..

Now you structure you company in such a way, that the company pays more money for the trademarks of your partner company, than you make.

Now of course, that is something a small company with 50 people can't do.

So the company with 50 people can't make ends meet, and the company which makes 200 million, continous to make money hand over fist.

It is almost already the case. However, there is a loophole. To avoid crashing starting businesses, the current tax is on profits, not on revenues. What big internet companies like Google and Apple do is splitting their companies in several entities. One entity is making the revenues. The other is "administrative services". The administrative one, located in a low-tax country, bills (highly) the one that makes the revenues. So the revenues are made in rich european countries, but the profits are made in the low-tax ones. (The example is oversimplified, but you get the idea). This is clearly cheating, but it's legal. Europe didn't manage to close the loophole because of the countries who profit from it. And no single cheated country has yet acted because the US backs this behavior.

Considering only foreign ones (local ones are already covered), the first explanation I can find is that for most of them it would just be an expensive and pointless exercise.

The time and costs involved to setup, maintain and enforce such a system would be ridiculously high compared to what it would bring in.

Another answer (still only considering foreign businesses) would be that for companies making so little, the burden could be much greater, hindering their growth (and future taxability).

And that's just from the tip of my head

It's probably forbidden by EU regulations.

Then they would shift net profit to a more favorable environment, i.e. by paying some contrived royalties to the Irish sister company?

That's exactly what they are currently doing. Current tax law applies to profits, so they shift them to ireland.