In the US the cops actually need a search warrant signed by a judge. In the EU they only sometimes need one.
>Should we be moving to Singaporean services? Oh shit, similar concerns there
Really? I've always been under the impression that it is courts who issue search warrants in Singapore, not the police or prosecutors.
Also, what you're describing is still infinitely better than the European system! The cops get to issue the warrants themselves.
What you are claiming about European cops is also not uniformly true. A German police officer cannot "just" self-issue a search warrant.
Yes. The more worrying situation is that Hungary can just decide that their police officers can self-issue search warrants, and then send those around the EU in the form of EIOs.