From what I have read there was a procedure taught to 737 pilots some decades ago that could have addressed the issue of being unable to move the trim wheel due to high aerodynamic forces at high speeds. It boils down to releasing pressure on the yoke in order to be able to move the trim wheel. However, this procedure is no longer taught due to its antiquity and the unlikelihood of its ever being required. My guess is that the pilots found their efforts to manually move the trim wheel weren't working and they finally gave up on it, resorting to the only other tool they knew of that could move the stabilizer.
There's plenty of blame to throw around here. Neither Boeing nor the pilots are without fault, as is often the case in serious accidents. Boeing gave the pilots an awful system and inadequate systems knowledge, training, and procedures to deal with what they eventually faced. The pilots failed to control airspeed and thrust while dealing with the emergency situation.
I hope that I would do better if placed in the same situation. But as a fellow professional I think it's arrogant to claim that I would do better without having been in that situation myself. We all are human and have a limited capacity to process information. Almost every crash of the past several years dating all the way back to AF 447 tells us that pilots are capable of being overwhelmed and losing their fundamental flying skills when presented with a startling or time pressured emergency scenario. Should we do better? Yes. Will we? Only those of us who have been through similar scenarios and come out alive can make that claim with certainty.