...so do(es the) military teach a safe EFATO turn back procedure??
Short answer - Yes.
Longer answer - It teaches you that there is a period shortly after take off where you often have few if any options. Conversely, students are also taught that if they have the failure some time later they have sufficient speed and/or altitude that they may have many options.
The critical part is teaching low experience pilots that a failure in that crucial transition section, where speed and alt are neither ideal or in abundance, can kill you if you stuff up and don't make the correct decision or handle the aircraft correctly.
There's no hard and fast numbers in general, ie your 500', as different aircraft have very different capabilities. But they all hurt if you f**k up!