Why might pilots continue a takeoff after an engine failure past V1, the reject-or-continue decision speed, instead of braking immediately?

Answer: Runway left may be too short

Runway left may be too short ✓ — Right. V1 is a runway-performance boundary, not a bravery switch. Before it, the aircraft should be able to reject and stop within the available distance; after it, continuing may be the safer certified path because stopping space may be gone. The twist is that an engine failure can make 'go' the planned safety answer.

Lift is already guaranteed — No. Lift is never guaranteed just because a speed callout has passed; the aircraft still has to rotate, lift off, and climb. The takeoff-speed rules include margins for control and climb, including engine-out cases. That is more subtle than 'the wings are fine now': the whole takeoff path has been planned around what remains possible.

One engine cannot climb — No. For transport airplanes, the takeoff-speed plan includes engine-out control and climb requirements; that is why V1 matters in the first place. One engine failing is serious, but it does not automatically make climbing impossible. Past V1, the certified plan may be to continue because stopping distance has become the limiting danger.