One fine day in the 1960s, I was taking off for my final check ride with the CFI, Les Phillips, before going solo at Sleap in an Auster Autocrat. (This was a club requirement, and a very good idea.)
At 400' or so, just crossing the boundary, the engine stopped. Before I had even realised that it wasn't Les chopping the power as a training exercise/test, and while I was still pushing the nose down without turning, he shouted "I have control", did a diving 180 turn without losing any airspeed, rolled out and touched down on the grass, downwind. (I then did my first solo, 10 minutes later, in the other club Autocrat.)
Landing anywhere in the "approved" area straight ahead would almost certainly have killed us both, as it usually will ever since airfields are no longer placed in open countryside.
He was an ex-RAF pilot and instructor, and I believe flew Spifires during WWII.
Ever since then I have preached the gospel that the mantra "Land straight ahead" should have been replaced decades ago by teaching ab initio pilots when and how to turn back after an engine failure on takeoff in a single.
The word "When" is important; part of the lesson is calculating a minimum height for the 180 diving turn, and knowing not to attempt the manouevre below that height. Given that, the manouevre should be taught and practised.
So I'm with Lomcevak.
Stand by for incoming!