Who cares if it's a densely packed city! A Performance 'A' category aeroplane should climb away with one out... They didn't aviate; that's why people are pontificating about it
I think you are assuming:
1. that the cockpit indications were not contradictory;
2. that it was possible accurately to identify the failed engine whilst the situation was still retrievable; and
3. that the crew's actions had the effects intended.
As far as I can understand from the thread so far, including analyses made here of the FDR data, none of these assumptions have been established as fact.
I think we are likely to find that the crew was desperately trying to aviate based on their interpretation(s) of the information available to them, and was perplexed that the actions they took didn't have their intended effects.