CompuChip is right, if the beams cancel in some place(s), they must constructively interfere somewhere else in order to conserve energy.
I never heard of experiments with light beams whose purpose was to confirm energy conservation. But we can look at specific examples, like the one depicted in Post #1, and show why we can't have cancellation everywhere.
Looking at the picture in Post #1, suppose there is a point within the beam-overlap where we have cancellation. That is, there is a 180 phase difference between the 2 beams at that point.
Now all you have to do is move 1/2 wavelength along one of the beams, so that the phase will change by 180 degrees for that beam. But for the other beam, you are moving across the beam and so there is no phase change for this second beam.
The net phase change is then 180 degrees. Coupled with the initial 180 degree phase difference, there is zero phase difference (i.e. complete constructive interference) in this 2nd location.
Regards,
Mark