I guess there are a couple of other factors also tied into that, aside from the work-life balance and corporate identity issues. One is maybe to do with the previous point about healthcare, which in the US will also be heavily dependent on your job. And so indirectly that also tends to make your working identity more inseparable from your personal self - in a medical emergency, the job you do, and the associated heath benefits or lack of them, might be the difference between life and death.
But there's also the British awkwardness about discussing money, especially with strangers. If I ask you your job, I am by implication asking you to give a ballpark figure as to how much you maybe earn, which is a complete social no-no in Britain. And rightly so in my view. But then I'm British...