If I may add to Old Smokey's observations
(1) a presumption is that the escape path is reasonably "flyable" .. not much point in an already high operational workload scenario to load the crew up to the point of excess overload
(2) while most runways can be addressed by a simple turn, some require moderately complex procedures which present a number of design problems, quite apart from considerations of crew workload. These might includes things like
[list=a][*] the need to define the centre of the turn radius[*]suitable lead .. how does the pilot determine this point ?[*]what radius of turn do we need ... bank less than 15 deg ? allowance for radius variation throughout the V2 range.[*]how do we achieve the required track ? aid errors ? DR ?[*]allowance for wind, aid and tracking error vs sensible expansion of the obstacle trapezoid[*]the additional trapezoid complexity and associated problems with defining which obstacles are inside the area of interest[*]obstacle data reliability, errors .. do we need to do a separate survey ? .. are there other than the normal sources of data avalable ?[/list=a]
The list goes on and on ... hence the usual desire for KISS.
So far as maintaining extended centreline might be concerned, it is VERY important that the crew do their absolute best to maintain the centreline of the presumed tracking trapezoid .. while the rules vary a bit according to which regulatory document is relevant, NONE of the trapezoids is wide enough to cater for slack crew attention to tracking.