Ref B737 family. 15 Bank Angle is likely only required if flying < V2 +15. This a manoeuvre margin certification issue reflective to Vs. It applies to any time time you are below this speed for the flap configuration. This will apply with an engine failure on takeoff and when an 'emergency turn' is required. It should be required until the first turn is completed and above MFRA. The 1500' consideration could come from obstacle clearance only being considered up to 1500' above the airfield. It is true that less bank angle = better climb performance, but that comes into the obstacle clearance calculation and any emergency turn routing and MFRA requirement.