I think I understand the decision to put the gear back down right away (though I don't think it's the first thing I would have thought of in such a scenario) and certainly appreciate that the German team cited in a similar incident used standard procedures and SOP to get their bird safely back on deck.
What I cannot get my brain around is why, with an engine failure just after lift off, the good engine wasn't at full power (this is not a propeller driven aircraft) until landing profile for whatever runway they could get to was assured. Even with the gear down, full power might have helped them get a few more feet under them as the sorted out their situation.
Once the left engine had its poultry meal, wouldn't a desire to at least get to MSA be pretty high on your list of priorities?
If yes, then why not use all of the horsepower one has to do so?
All above considered, it's hard to argue against the criticisms on training.
If SOP and Flight Manual call for a "keep it clean, climb, level off, then trouble shoot, then configure, then land" there's a training issue to address that the company ought to take a hard look at.
Another of their crews may learn the wrong thing if the "these guys made it, but there was a simpler and safer way" lessons isn't strongly emphasized.
If other crews in the airline learn the wrong lesson from this (tip cap to "hero pilot" issue) then the chance that the next unexpected poultry meal on take off ends in tears increases.
