when a captain has to be a captain
I would suggest that is all the time.
However, NO-ONE can eyeball a limiting OEI departure in a critical terrain environment - the subtended angles are too shallow for reasonable human perceptual considerations (I may be on suspect strict physiological/psychological ground there ? perhaps some of the relevant techo specialists can advise if the research literature indicates that the typical human can discriminate to that sort of minimal angular displacement ?) ergo, either one has had the takeoff analysed or one is on dangerous ground - and, potentially, literally.
and slowed to V2
every now and then an event written in blood results in great Industry systems change. The 10 was one .. AF another. Just goes to show that we don't have all the bases covered at the start.
The last two operators I have flown with had a procedure to fly runway track in the event of an engine failure at or soon after V1(which easily applies to most runways in my experience) unless there is an engine out special procedure.
Sounds pretty reasonable on the face of it.
My question is simply, how far out past the end of the runway are obstacles required to be assessed, if there is a requirement.
The usual rules are
(a) for the entire flight
(b) specifically, for the takeoff, until either the takeoff is completed (nominal 1500ft) or until the en-route rules can take care of the problems .. which may be further downtrack.