Not really as simple as that, I'm afraid.
(a) the usual takeoff should only be used for takeoff OEI if your performance folk have done the sums for OEI, as they should have, determined and published words to the effect that the departure is acceptable for OEI.
(b) if the normal takeoff doesn't work for OEI, then there should be published an acceptable escape procedure for takeoff.
(c) when it comes to the miss, neither of the above necessarily fit the profile for the miss (or vice versa, if you prefer). Reasons will relate to speeds, turns in relation to specific terrain (speed/radius of turn) configuration and changes, and position in respect of the runway at the commencement of the miss, tracking and tracking accuracy and so on. That is to say, unless the performance folks have done some sensible sums, and published a way out, you can't necessarily presume that this or that will be acceptable and work.
(d) do all operators look after this stuff ? Not for me to opine - however, for my customers the answer is yes. Same for Old Smokey, Mutt and other ops engineers who have an understanding of frights from the cockpit ....