Repair of big cuts and lacerations is a race against the clock. Over a fairly short timeframe the edges of the cut start to curl and heal — nature is always hard at work and will not wait.
The general rule is that cuts and lacerations need to be closed within about 8 hours or less — sooner if on the face.
IF you wait, the doctor in the ER has to cut NEW FRESH EDGES on your existing cut. Disgusting, but true. Or, the ER may refuse to close the laceration at all.