So, one armchair laser physicist to another, here’s my theory on why I think you’re right, but your reasons why might be off:
While this is the basic gist of what is happening, I don’t think the logic makes sense – I think you reached the correct end result without the correct underlying causes. Diffuse light sources and laser sources are fundamentally different. With collimated laser light, the light density is much more uniform than with a point source like a typical led or filament, and using a lens to shrink it down to a pinpoint makes for a very uniform end image – there is no “out of focus” or “brighter” areas, it’s all one very small, very intense circle of infrared light.
Where I think the logic gets back on track is that you do see more power in the center of your laser pass versus the edges. I think that’s more down to the fact that it is a circle. I did an illustration of my take on the physics of that situation, let me see if I can find it. Here we go:
So yes I think the individual passes show power fall-off on the edges, but I don’t think it has much to do with the focus. it’s more about laser residency time on any given point as the laser passes by. In the end, I’m not sure that this is anything other than academic, we know this is how it behaves so the reasons why are less important.