Mutt, my good friend, g'day ... I knew it wouldn't take long to get a bite on this point.
Short answer, as you well know, is ... "it depends"
(a) if the AEO and OEI paths are the same .. no worries
(b) if the OEI turns away from a reasonably distant obstacle and the rest of the area is benign ... usually no worries
(c) consider, though, a case where the takeoff is from within a valley with only one feasible OEI escape path through a saddle which can only be achieved by a turn shortly after takeoff. The AEO departure is over tiger country. V1 cut .. no worries ... track via the escape. But what about if the failure occurs AFTER the turn point for the V1 plan ?
(i) do we just say ... " tough luck" and order a replacement hull ?
(ii) do we just say ... "problem belong pilot", call the company's defence legal team, and prepare to hang the pilot out to dry ?
(iii) or should we have thought about that late failure case ? or perhaps have scheduled ALL takeoffs via the OEI escape track ?
Many runways fit into the spectrum between (b) and (c) ...
As to actually doing the sums, I have never had any major problem in setting up a reasonably simple PC program to do the analysis ... monitor the presumed AEO performance and then consider the options in the event of a failure. Certainly not a five minute exercise but, nonetheless, not technically difficult. If the AFM has not gone through the regression exercise and you don't have an OEM program ... it can get a bit frustrating ...
... as a for instance ... I can recall one runway where the options were
(a) takeoff over the saddle located some distance off the runway end and wear the payload losses
(b) schedule a turn at runway head
I spent days doing the thing manually looking for a VMC departure which got around the OEI losses involved in the straight ahead takeoff (aircraft MTOW permitted a reduction in splay width in the particular country) ... eventually I had to admit defeat and just run with the straight flight path.
.. as another for instance ... I have done a number of schedules from a medium elevation airport surrounded by lots of bumpy bits .. in this case, the critical failure for one of the main runways was very definitely some distance out ... the V1 cut was not very relevant for continued flight path obstacle clearance.
But the point is ... is it acceptable just to run the V1 failure analysis and merely presume that the AEO track is immune from OEI problems ? ... without at least having a think about the thing on a runway by runway basis ?