I have a few theories for this, and this is how I've explained it when asked. The first one is that it gives them the opportunity to hang you if you're blatantly busting minimums. If you shoot the approach and it's been 1/8SM FG all day, and you magically make it in, and you say "well I had the ALS in sight, then went down to 100'AGL and saw the threshold lighting so I landed," this gives them the opportunity to say, "BS! There's no way you saw that, 91.13 and you were lying, go directly to jail, do not pass go, do not collect $200."
Second, remember that it doesn't talk about landing with less flight vis so much as it talks about "operating below DA or MDA or continue an approach below DA/DH," there are places where there aren't ILSs to 200 and 1/2 left and right, imagine an approach with outrageously high minimums. In these places, it could very well be that the approach has a visibility requirement that is based on the ability of the airplane to maneuver and meet terps on a missed. So, you go to one of these airports, and let's say the plate calls for 4SM of vis, you fly into there and at the MAP there's only 3SM miles of flight vis, but you keep going, because "F-it, it's VFR!" and you then you realize that the actual runway is completely fogged in and there's no way you can land or a moose is on the runway or whatever. The problem is now that you cannot see far enough ahead to avoid obstacles on the climbout (since at 120kts on the missed 3NM is only 1.5minutes) and you impact a mountain, or -potentially more sketchy - you can't fly the published missed because you're already too far off the path during your circling maneuver and have to make it up on your own because you can't see far enough ahead to dodge pointy rocks. Here are a few approaches where I think this applies and is worth mentioning:
http://155.178.201.160/d-tpp/1307/06213LDADH.PDF (Note that the MAP is 5.2NM from the field, and the vis mins are 5SM)
http://155.178.201.160/d-tpp/1307/09292RA.PDF (Note that this approach requires you to "fly visually for 5.2 NM" into the airport)
http://155.178.201.160/d-tpp/1307/01191LDAX8.PDF
Now the Juneau one is really the most interesting plate and worthy of discussion. Consider where the missed approach point is. 2.2 DME from the runway. Consider the following situation. You're out over the water before MOLRE at 1880' exactly - just like a good boy. Also imagine that the visibility is great but the ceiling is crummy over the actual airport (1000'ish). You can see the approach lights, and start down to do your "normal descent" but as you start down (now past MOLRE) you realize that the vis inside of the bowl is much lower. The Feds want you to be able to have the visibility to maneuver out of whatever situation you've gotten yourself into. As soon as you recognize that you don't have the vis required you have to cob it and go missed, because the guys who write approaches want you to be able to have a maneuvering budget.
http://155.178.201.160/d-tpp/1307/06367GE.PDF (this approach into DUT shows a similar situation).
Finally, I've experienced whiteout that wasn't visible until I was only a few hundred feet above the ground - that is to say the aairport was distinctly visible until I got close - then it went away. The Feds want you to run away when this happens - they don't want you to try to save it - just go missed.
