I'd always thought V2 is a performance issue with all Perf A a/c. It is 'never below speed'; takeoff safety speed in old speak. Is it not related by various % to Vr & VMCA and perhaps many other speeds? It is a certification & performance speed for many types, as it is a concept.
Now for B737, and perhaps others, >V2+15 = full manoeuvrability.
One is vertical for all aeroplanes, the other is lateral for B737.