Do photons collide with each other?

There is zero energy where the waves are cancelling. Putting a target up where the beams are perfectly destructively cancelling would show nothing. There would be no illumination, and certainly no damage.

BTW, getting a laser that will punch a hole in something even as slight as a piece of paper isn’t cheap.

It’s all still really there. For any conceivable laser and lens combination you are unable to get destructive interference without an equal amount of constructive interference.

I missed this part. You won’t necessarily zap what’s there, because the constructive interference will probably occur away from the target.