One other factor that influences energy management and sightline angle and which has not yet been mentioned is wind. When we cleared the Tucano to fly in a 40 kt surface wind one of the most interesting points was that when using the normal 1500 ft Low Key abeam the Initial Aim Point it was not possible to make a touchdown at the IAP; a 2000 ft Low Key was required, almost independent of the wind direction.
When the Hawk T1 entered service the bad weather engine failure profile taught was the '1 in 1' profile of the Hunter whereby you were vectored towards the runway centreline and when established on it and the range to touchdown in nms equaled the height in thousands of feet then you lowered the landing gear . Airspeed was then varied around the nominal glide speed (165 KIAS) to stay on the '1 in 1' slope and when visual with the runway the flaps were lowered when required to make the desired touchdown point. However, although this worked satisfactorily with idle thrust, at some stage it was realised/identified/confirmed that with a windmilling engine the drag was too high and it could not maintain the '1 in 1' profile. The result was that the radar Forced Landing pattern was developed. I am not sure precisely when but the radar FL/PFL was not taught when I was a student at Valley on the Hawk in early 1978.
Most engine problems for real do not require an engine shutdown nor involve a total loss of thrust which often makes diagnosis difficult and choosing the optimum course of action difficult. In some cases, what is needed from the engine is to drive the electrical and/or hydraulic system more than to generate thrust. Typically, a low power setting will load an engine less than a high one such that the engine may be kept running for longer at idle, or a little above it, and favouring a precautionary forced landing pattern to a fixed power approach if feasible (although this is very type specific). This becomes a critical decision following an EFATO; do you turn back to the reciprocal of the take-off runway, climb to/decelerate towards low key or fly a fixed power approach? The best decision will be on a case-by-case basis but practising all options will give you the best chance of success. However, if you lose more aircraft practising some of the more marginal profiles such as turnbacks than you will save if you get it right for real then the practise is, perhaps, not justified. The pros and cons of practising EFATOs, turnbacks, low energy PFLs etc is not black and white.