I think the confusion for many in common law jurisdictions is that here, if a court finds probable cause, it issues the arrest warrant; the prosecutor has no such authority.  And it's kind of a big deal because I personally have dealt with several situations where cops have tried to intimidate clients with "warrants" they issued themselves.  Hence we are leery of any warrant issued by an enforcing authority rather than a tribunal.

As a side note, I think the inherent differences between common law and civil law systems (which were never identified and addressed when Maastricht was being hammered out) provided much of the grist for the "We have to take control back from the Brussels bureaucrats" elements of the Brexit campaign.