flyburg,
I attempted to be as accurate as I could in my post; I referred to “… a better performance profile”, whereas you discuss “… better climb performance”, which I interpret as instantaneous climb gradient.
The obstacle clearance profiles are based on climb gradient with an engine failing at V1. An engine failure at any time after V1 puts the aircraft in a more advantageous ‘altitude’ position; but the crew do not know what the value of that is.
I agree with you; if below V2 accelerate to V2 and climb at V2, if above V2, say V2+10, then maintaining that speed should meet all of the initial performance requirements, but specific issues in company published emergency turn procedures should be checked.
With an engine failure above V2+10, the aircraft should similarly have an advantage, but without knowing the speed excess or altitude advantage gained so far, then the crew may wish to fly V2+10 or Vfto. My post might not have clarified these details.
However, harsh or rapid pitch manoeuvring should be avoided in order to achieve a slower speed, (cf DC10 Chicago accident), and in most circumstances a large speed reduction would not be required as such scenarios are more likely after commencing a normal departure route; then the aim is to meet the gradient requirement in that procedure. IIRC one of the normal departures from Lugano had several emergency climb break points, rerouting the normal departure to one of several alternative emergency engine-fail procedures with speed requirements.