As a life-long Wilson fan I have to agree that while JITNEY is a wonderful play -- probably his most enjoyable to sit through -- Becker's death is not its finest moment. Wilson used this technique more than once (it re-appears in TWO TRAINS RUNNING with the character of Hambone) and it is never completely satisfying.
As to the gun going off, although Wilson can hardly have planned it this way, you could argue, and I would, that in the ten play cycle, the gun does finally go off -- in KING HEDLEY II. The threat of violence hangs over all the plays, but if you want the payoff, you have to see them all. When the Kennedy Center did barely-rehearsed versions of all 10 and you could see them sequentially in a compact period of time, the sense of the gun being drawn and eventually going off was very palpable.