How about-aim small, miss small.
A BIG dot give more room for missing??
How about aim small, hit small. There is no reason to aim to miss.
For self defense shootings, a golf-ball sized dot would give you a golf would cover a very specific POA and no matter how much you moved around, if the dot was on the POA and the gun sighted to the dot, the POI within 1.6" of the intended POI. That would be a giant laser dot, but great shooting for virtually any self defense shooting.
The cool thing about a larger dot is that your gun could literally be on target at much greater distances where your shot could be in the dot and not just somewhere near the dot from closer to contact to further out. A larger dot would also allow for parallax problems introduced into the windage via lateral tilting of the gun during firing further than a small dot.
A big dot is just easier to find and see (assuming same intensity) than a small dot and during a high stress situation, critical time can be lost when one is "hunting the dot."
So for self defense and at self defense distances with a handgun, a larger dot could be a very good thing, but as noted, there are some serious laser size and power issues at hand that would preclude it from working.
Remember too that lasers were never designed for use on defensive handguns. They're not meant for you to quickly acquire the red dot and blast away at center mass on Joe Crackhead.
Lasers were designed for training purposes to teach people how to acquire and properly align their sights. I tell my students that lasers (and flashlights) do not belong on defensive handguns, for a variety of reasons.
Whether or not a laser belongs on a firearm has nothing to do with the design intent. The first firearms were not designed with sights, so by extension it could be argued that guns should not have sights.
It is interesting that you say they weren't put on guns for sighting, but to learn how to align sights. Lasers had been used for weapon sighting years before they appeared on pistols. I don't see how the transition to pistols changed anything, but if you have some good source material, I would enjoy reading it.
The earliest handgun laser sight patent I find is from 1990. It is stated explicitly that it is for improved sighting and does not mention using the sight for sight alignment training.
http://www.patentstorm.us/patents/6591536/description.html ...just in case design intent is still being argued...