In TOS, approaching starships were usually barely if at all visible as a dot unless the viewscreen was heavily magnified - that's what you're trying to hit with this "shotgun".[\quote]
And yet, the Enterprise did just this during the TOS episode
Balance of Terror, and damaged the Romulan Warbird badly. Silly or not, you can do it. (It should be noted that phasers aren't hit-or-miss, you "slash" the beam through an area, unlike photon torpedoes or disruptor bolts.)[\quote]
That actually makes sense. Or the torpedo could convert into a much larger, less intense bolt which covers a broader area.