Slippery Pete...
Broadly, I agree. But with the proviso which you alluded to: namely, that this advice pertains to modern aircraft only. Maybe. There remain sufficient CV580s, Electras, C-130s, HS748s, and their smaller cousins to narrow your emphasis to the more modern versions only, at best.
In the earlier generation of turboprops the acceleration altitude was typically 400', and that for good reason. I have had a few actual powerplant failures in T-56* engine/Aeroproducts 601 propellors to testify to the need for timely intervention. PW engines too. **But those were primitive installations (and times) compared to the engine/props relevant to this discussion.
* Allison 501-D13 in civilian application
The propellor makes a thrust loss so much more demanding than on a jet: the ability of a windmilling prop/engine to extract all the energy that the good powerplant is producing (made worse with acceleration) is not understood by the jet only guys, and their advice should be taken with a grain of salt, if in fact you can identify it as such. Not all transport aircraft are created equally, nor is all transport aircraft experience.
Anyway...lots of suppositions in this thread, not much emphasis on confirmation bias about a heavily taxed crew already concerned about No.1, then faced with an auto fx on No.2. Most accidents, properly considered, end up being a study in perceptions and indications. I don't expect that this one will be too different.