The surveillance systems in the EU are just as invasive, and frequently moreso, than in the US.

This is largely a false meme, an urban legend. There is no meaningful privacy difference between Europe and the US.

This is simply a money grab; it won’t move the needle on privacy one bit. You’ll still be surveilled everywhere you go in Europe by the state, the mobile operators, and most of the other apps on your phone.

Furthermore, it doesn’t matter if the data stays inside the EU or not. Google collects the same data and the US intelligence agencies can compel them to access the data on EU citizens, stored on EU-located Google servers just the same as if it were in Mountain View.