Drift alert!
there obviously is such a point but we don't teach it.
I got myself into hot water expounding in Flight, eons ago, that every pilot, PPL and upward, of a single-engine aircraft should be taught how to calculate, for each take-off with weight, wind, temp etc factored in, the point at which it is safe to turn back after an EFATO.
Practising the steep diving turn and downwind landing should also be an essential feature of the basic SEP syllabus, once pilots understand when to use it and when not to.
Pilots should be taught to
calculate whether they can safely land ahead after an EFATO at any point up to that height. If they cannot, they must positively change things so that they can, by reducing weight, start the roll from futher back if that's possible, or waiting for a stronger headwind.
If they do not do all that, all they are doing is hoping like hell that an EFATO won't happen, because if it does and they haven't reached the point where a turn can be done, their straight-ahead landing will probably be into a housing estate. And if they try the turn and have not been taught to do it properly, they'll almost certainly stall and spin in the turn and kill themselves that way.
Every time I hear ATC instructing a usually willing single-engine pilot to "use the intersection" I cringe, because neither seems to understand the danger. Multi's are fine, so long as the reduced TORA, TODA and ASDA are OK for them, but many PPLs appear to think that what's long enough for a B737 must also be long enough for their little SEP with 4 up, bags and a full tank. It isn't, if they have an EFATO and have to land ahead from 400 ft.
Alan Bramson called it "The Impossible Turn", and that's what I wrote against all those years ago. But it isn't impossible; it just needs to be properly taught; ie, when and how. The straight ahead mantra was fine when most airfields had fields all around them instead of housing. It's time now to stop pretending that it's OK to teach a procedure that will probably kill anyone who actually follows it assiduously.
Reliability is now so good that the probability of mechanical failure is very low. But what about human error?
Sorry about the drift!