During early morning hours, most people are in bed, and not anticipating a visit from the police. To oppose the officers or agents sent to arrest them, they have to overcome the cobwebs that sleep brings, and that gives the cops a reaction time advantage.
The objective in serving an arrest warrant is to get the named person in custody with as little fuss as possible. If the person is someone who might try to resist arrest, flee the scene, or oppose the cops with force, it’s best for everyone that the cops come when their guard is down.
They’re going to be arrested eventually, and it’s better to do it without anyone being hurt. Unless the person to be arrested is a fugitive, actively hiding or running from the cops, service of an arrest warrant can be done in a much more civilized manner.
The investigator holding the warrant calls the person to be arrested, or, preferably, their attorney. They arrange a time and place for the person to surrender themselves to the police.
The arrested person can be accompanied by their attorney to ensure their rights are not violated, and bail (if permitted) can be arranged in advance. The arrested person can surrender, get booked, and be out the door in an hour or two with a court date to appear later.