You generally can't operate a running business in EU or any other country out of the Caymans. You could have share holding companies registered there but to act

You generally can't operate a running business in EU or any other country out of the Caymans. You could have share holding companies registered there but to actually run a physical business, you have to actually have a company registered in the market (or come in as a purely imported product) Ireland works simply because it is a member of the EU and any EU HQ business can operate anywhere else in EU.