You're misunderstanding the goals of the EU. The EU only cares about limiting their grip as a result of their main goal. The main goal of the EU is to protect the rights of their citizens, which they do by enforcing existing anti-monopoly laws.

The EU has in principle no problem with a company gaining giant market share by providing a successful service or product. There would be no problem if Google or Apple would gain 99% market share by everybody voluntarily choosing their product. But it is a problem if they then use that marketshare to make it harder for competitors to compete.

I.e.: you're wrong to say that they're trying to minimise the 'grip' they have. They are merely trying to prevent companies abusing that grip.

That being said; I'm pretty sure that the EU does actually fund a lot of open source development