Yes, I agree up to a point. The power of arrest without warrant is old, but there are other requirements. There has to be a reasonable suspicion or belief on the behalf of the arresting constable that the individual has committed a crime.
The basis of an arrest on warrant has to be that the constable or appropriate person has reasonable cause to believe that a warrant is in existence for that person. That is normally done by the constable radioing back to the station and being told that a warrant is held in the Scottish Criminal Record Office or the English version of it. Once the person is taken back to the police station, they can be shown the warrant then. I do not see why a European arrest warrant should come under a different system.