The first few seconds after the hook up are possibly the most critical moments of the battle. Marlin will often shake their heads vigorously the moment they feel the sting of the hooks.
The slack line created after the line releases from the outrigger is often all that a marlin needs to free itself.
Tag lines are lengths of cord that cut out the drop back, reducing the chances of a fish throwing the hooks. When you think about it there is little sense in having slack line at such a critical point.