A primary component of the American Dream is economic or financial success. There is also the idealistic notion of "dedicating yourself thoroughly, and 'making it' through hard work and persistence," but without the addition of financial success, it doesn't really work.
Not only has Bernard done his time with relation to his studies, advancement, and professional distinction, he is also "special" as a lawyer, and wealthy because of it. This counters Willy's perception that one succeeds merely by being well-liked, particularly as it relates to his earlier perception of his sons, Biff and Happy, and the neighbor's boy, Bernard, who, at the time, wasn't "well-liked."
While Willy struggles with the pressures of work and family, his mood swings become indicative of a deteriorating mental state. This foreshadowing is confirmed by his suicide at the end of the play, but the reader or audience member still has to grapple with the irony that although Willy wanted his family, specifically Biff, to benefit financially, it is the classification of suicide that prevents them from receiving the money. They lose Willy and yet are "free" from him, but at the same time, they lose out on any sense of future financial security.